The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a
parameterization
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, de ...
of the
Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
cosmological
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
model in which the universe contains three major components: first, a
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
denoted by
Lambda
Lambda (}, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the voiced alveolar lateral approximant . In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoenician Lamed . Lambda gave rise ...
(
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
Λ) associated with
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
; second, the postulated
cold dark matter
In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a sm ...
(abbreviated CDM); and third, ordinary
matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
. It is frequently referred to as the ''standard model'' of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:
* the existence and structure of the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
* the
large-scale structure in the distribution of galaxies
* the observed
abundances of
hydrogen (including deuterium), helium, and lithium
* the
accelerating expansion of the universe
Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered durin ...
observed in the light from distant galaxies and
supernova
A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or when ...
e
The model assumes that
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.
The ΛCDM model can be extended by adding
cosmological inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularit ...
,
quintessence, and other elements that are current areas of speculation and research in cosmology.
Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are
modified Newtonian dynamics
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining ...
,
entropic gravity
Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes gravity as an ''entropic force''—a force with macro-scale homogeneity but which is subject to quantum-level disorder—and not a fundamental intera ...
, modified gravity, theories of large-scale variations in the matter density of the universe,
bimetric gravity
Bimetric gravity or bigravity refers to two different classes of theories. The first class of theories relies on modified mathematical theories of gravity (or gravitation) in which two metric tensors are used instead of one.
The second metric may ...
, scale invariance of empty space, and decaying dark matter (DDM).
Overview
The ΛCDM model includes an expansion of metric space that is well documented both as the
red shift
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
of prominent spectral absorption or emission lines in the light from distant galaxies and as the time dilation in the light decay of supernova luminosity curves. Both effects are attributed to a
Doppler shift
The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...
in electromagnetic radiation as it travels across expanding space. Although this expansion increases the distance between objects that are not under shared gravitational influence, it does not increase the size of the objects (e.g. galaxies) in space. It also allows for distant galaxies to recede from each other at speeds greater than the speed of light; local expansion is less than the speed of light, but expansion summed across great distances can collectively exceed the speed of light.
The letter Λ (lambda) represents the
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
, which is currently associated with a vacuum energy or
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
in empty space that is used to explain the contemporary accelerating expansion of space against the attractive effects of gravity. A cosmological constant has negative pressure,
, which contributes to the
stress–energy tensor
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress ...
that, according to the general theory of relativity, causes accelerating expansion. The fraction of the total energy density of our (flat or almost flat) universe that is dark energy,
, is estimated to be 0.669 ± 0.038 based on the 2018
Dark Energy Survey
The Dark Energy Survey (DES) is an astronomical survey designed to constrain the properties of dark energy. It uses images taken in the near-ultraviolet, Visible spectrum, visible, and near-infrared to measure the expansion of the universe using ...
results using
Type Ia Supernova
A Type Ia supernova (read: "type one-A") is a type of supernova that occurs in binary systems (two stars orbiting one another) in which one of the stars is a white dwarf. The other star can be anything from a giant star to an even smaller white ...
e or 0.6847 ± 0.0073 based on the 2018 release of
''Planck'' satellite data, or more than 68.3% (2018 estimate) of the mass-energy density of the universe.
Dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ab ...
is postulated in order to account for gravitational effects observed in very large-scale structures (the "flat"
rotation curve
The rotation curve of a disc galaxy (also called a velocity curve) is a plot of the orbital speeds of visible stars or gas in that galaxy versus their radial distance from that galaxy's centre. It is typically rendered graphically as a plot, and ...
s of galaxies; the
gravitational lens
A gravitational lens is a distribution of matter (such as a cluster of galaxies) between a distant light source and an observer that is capable of bending the light from the source as the light travels toward the observer. This effect is known ...
ing of light by galaxy clusters; and enhanced clustering of galaxies) that cannot be accounted for by the quantity of observed matter.
Cold dark matter
In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a sm ...
as currently hypothesized is:
;''non-
baryon
In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...
ic'': It consists of matter other than protons and neutrons (and electrons, by convention, although electrons are not baryons).
;''cold'': Its velocity is far less than the speed of light at the epoch of radiation–matter equality (thus neutrinos are excluded, being non-baryonic but not cold).
;''dissipationless'': It cannot cool by radiating photons.
;''collisionless'': The dark matter particles interact with each other and other particles only through gravity and possibly the weak force.
Dark matter constitutes about 26.5%
of the mass–energy density of the universe. The remaining 4.9%
comprises all ordinary matter observed as atoms, chemical elements, gas and plasma, the stuff of which visible planets, stars and galaxies are made. The great majority of ordinary matter in the universe is unseen, since visible stars and gas inside galaxies and clusters account for less than 10% of the ordinary matter contribution to the mass–energy density of the universe.
Also, the energy density includes a very small fraction (~ 0.01%) in cosmic microwave background radiation, and not more than 0.5% in
relic neutrinos. Although very small today, these were much more important in the distant past, dominating the matter at redshift > 3200.
The model includes a single originating event, the "Big Bang", which was not an explosion but the abrupt appearance of expanding
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
containing radiation at temperatures of around 10
15 K. This was immediately (within 10
−29 seconds) followed by an exponential expansion of space by a scale multiplier of 10
27 or more, known as
cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity ...
. The early universe remained hot (above 10,000 K) for several hundred thousand years, a state that is detectable as a residual
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
, or CMB, a very low energy radiation emanating from all parts of the sky. The "Big Bang" scenario, with cosmic inflation and standard particle physics, is the only current cosmological model consistent with the observed continuing expansion of space, the observed distribution of
lighter elements in the universe (hydrogen, helium, and lithium), and the spatial texture of minute irregularities (
anisotropies
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
) in the CMB radiation. Cosmic inflation also addresses the "
horizon problem
The horizon problem (also known as the homogeneity problem) is a physical cosmology, cosmological fine-tuning problem within the Big Bang model of the universe. It arises due to the difficulty in explaining the observed homogeneity of Causality ...
" in the CMB; indeed, it seems likely that the universe is larger than the observable
particle horizon The particle horizon (also called the cosmological horizon, the comoving horizon (in Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from particles could have traveled to the observer in the age of the univers ...
.
The model uses the
Friedmann–Lemaître–Robertson–Walker metric
The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
, the
Friedmann equations
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedman ...
and the
cosmological equations of state to describe the observable universe from right after the
inflationary epoch
__NOTOC__
In physical cosmology, the inflationary epoch was the period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid exponential expansion. This rapid expansion increased the ...
to present and future.
Cosmic expansion history
The expansion of the universe is parameterized by a
dimensionless
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
scale factor
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a '' scale factor'' that is the same in all directions. The result of uniform scaling is similar ...
(with time
counted from the birth of the universe), defined relative to the present day, so
; the usual convention in cosmology is that subscript 0 denotes present-day values, so
is the current age of the universe. The scale factor is related to the observed
redshift
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in f ...
of the light emitted at time
by
:
The expansion rate is described by the time-dependent
Hubble parameter
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
,
, defined as
:
where
is the time-derivative of the scale factor. The first
Friedmann equation
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedma ...
gives the expansion rate in terms of the matter+radiation density the
curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
and the
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
:
where as usual is the speed of light and is the
gravitational constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
.
A critical density
is the present-day density, which gives zero curvature
, assuming the cosmological constant
is zero, regardless of its actual value. Substituting these conditions to the Friedmann equation gives
:
where
is the reduced Hubble constant.
If the cosmological constant were actually zero, the critical density would also mark the dividing line between eventual recollapse of the universe to a
Big Crunch
The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potential ...
, or unlimited expansion. For the Lambda-CDM model with a positive cosmological constant (as observed), the universe is predicted to expand forever regardless of whether the total density is slightly above or below the critical density; though other outcomes are possible in extended models where the
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
is not constant but actually time-dependent.
It is standard to define the present-day density parameter
for various species as the dimensionless ratio
:
where the subscript
is one of
for
baryon
In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...
s,
for
cold dark matter
In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a sm ...
,
for
radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:
* ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
(
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s plus relativistic
neutrino
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
s), and
or
for
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
.
Since the densities of various species scale as different powers of
, e.g.
for matter etc.,
the
Friedmann equation
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedma ...
can be conveniently rewritten in terms of the various density parameters as
:
where
is the
equation of state
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal ...
parameter of dark energy, and assuming negligible neutrino mass (significant neutrino mass requires a more complex equation). The various
parameters add up to
by construction.
In the general case this is integrated by computer to give
the expansion history
and also observable distance–redshift relations for any chosen values of the cosmological parameters, which can then be compared with observations such as
supernovae
A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or when a ...
and
baryon acoustic oscillations
In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe, caused by acoustic density waves in the primordial plasma of the early universe. In the same way t ...
.
In the minimal 6-parameter Lambda-CDM model, it is assumed that curvature
is zero and
, so this simplifies to
:
Observations show that the radiation density is very small today,
; if this term is neglected
the above has an analytic solution
:
where
this is fairly accurate for
or
million years.
Solving for
gives the present age of the universe
in terms of the other parameters.
It follows that the transition from decelerating to accelerating expansion (the second derivative
crossing zero) occurred when
:
which evaluates to
or
for the best-fit parameters estimated from the
''Planck'' spacecraft.
Historical development
The discovery of the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
(CMB) in 1964 confirmed a key prediction of the
Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
cosmology. From that point on, it was generally accepted that the universe started in a hot, dense state and has been expanding over time. The rate of expansion depends on the types of matter and energy present in the universe, and in particular, whether the total density is above or below the so-called critical density.
During the 1970s, most attention focused on pure-baryonic models, but there were serious challenges explaining the formation of galaxies, given the small anisotropies in the CMB (upper limits at that time). In the early 1980s, it was realized that this could be resolved if cold dark matter dominated over the baryons, and the theory of
cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity ...
motivated models with critical density.
During the 1980s, most research focused on cold dark matter with critical density in matter, around 95% CDM and 5% baryons: these showed success at forming galaxies and clusters of galaxies, but problems remained; notably, the model required a Hubble constant lower than preferred by observations, and observations around 1988–1990 showed more large-scale galaxy clustering than predicted.
These difficulties sharpened with the discovery of CMB anisotropy by the
Cosmic Background Explorer
The Cosmic Background Explorer (COBE ), also referred to as Explorer 66, was a NASA satellite dedicated to cosmology, which operated from 1989 to 1993. Its goals were to investigate the cosmic microwave background radiation (CMB or CMBR) of th ...
in 1992, and several modified CDM models, including ΛCDM and mixed cold and hot dark matter, came under active consideration through the mid-1990s. The ΛCDM model then became the leading model following the observations of
accelerating expansion in 1998, and was quickly supported by other observations: in 2000, the
BOOMERanG
A boomerang () is a thrown tool, typically constructed with aerofoil sections and designed to spin about an axis perpendicular to the direction of its flight. A returning boomerang is designed to return to the thrower, while a non-returning b ...
microwave background experiment measured the total (matter–energy) density to be close to 100% of critical, whereas in 2001 the
2dFGRS
In astronomy, the 2dF Galaxy Redshift Survey (Two-degree-Field Galaxy Redshift Survey), 2dF or 2dFGRS is a redshift survey conducted by the Australian Astronomical Observatory (AAO) with the 3.9m Anglo-Australian Telescope between 1997 and 11 A ...
galaxy redshift survey measured the matter density to be near 25%; the large difference between these values supports a positive Λ or
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
. Much more precise spacecraft measurements of the microwave background from
WMAP
The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic mic ...
in 2003–2010 and ''
Planck
Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.
Planck made many substantial contributions to theoretical p ...
'' in 2013–2015 have continued to support the model and pin down the parameter values, most of which are now constrained below 1 percent uncertainty.
There is currently active research into many aspects of the ΛCDM model, both to refine the parameters and to resolve the tensions between recent observations and the ΛCDM model, such as the
Hubble tension
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
and the
CMB dipole
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneity (physics), homogeneous and Isotropy, isotropic when viewed on a large enough scale, since the forces ar ...
.
In addition, ΛCDM has no explicit physical theory for the origin or physical nature of dark matter or dark energy; the nearly scale-invariant spectrum of the CMB perturbations, and their image across the celestial sphere, are believed to result from very small thermal and acoustic irregularities at the point of recombination.
Historically, a large majority of astronomers and astrophysicists support the ΛCDM model or close relatives of it, but recent observations that contradict the ΛCDM model have recently led some astronomers and astrophysicists to search for alternatives to the ΛCDM model, which include dropping the
Friedmann–Lemaître–Robertson–Walker metric
The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
or modifying
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
.
On the other hand,
Milgrom Milgrom is a surname derived from the Yiddish word for pomegranate (:yi:מילגרוים, מילגרוים, Milgroim) and may refer to:
* Al Milgrom, Allen "Al" Milgrom (born 1950), American comic book writer
* Felix Milgrom (1919-2007), Jewish Pol ...
,
McGaugh, and
Kroupa have long been leading critics of the ΛCDM model, attacking the dark matter portions of the theory from the perspective of
galaxy formation
The study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous universe from a homogeneous beginning, the formation of the first galaxies, the way galaxies change over time, and the processes that have ge ...
models and supporting the alternative
modified Newtonian dynamics
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining ...
(MOND) theory, which requires a modification of the
Einstein field equations
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were published by Einstein in 1915 in the form ...
and the
Friedmann equations
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedman ...
as seen in proposals such as
modified gravity theory
Modified may refer to:
* ''Modified'' (album), the second full-length album by Save Ferris
*Modified racing, or "Modifieds", an American automobile racing genre
See also
* Modification (disambiguation)
* Modifier (disambiguation)
Modifier may re ...
(MOG theory) or
tensor–vector–scalar gravity
Tensor–vector–scalar gravity (TeVeS),
developed by Jacob Bekenstein in 2004, is a relativistic generalization of Mordehai Milgrom's Modified Newtonian dynamics (MOND) paradigm.
The main features of TeVeS can be summarized as follows:
* As i ...
theory (TeVeS theory). Other proposals by theoretical astrophysicists of cosmological alternatives to Einstein's general relativity that attempt to account for dark energy or dark matter include
f(R) gravity
() is a type of modified gravity theory which generalizes Einstein's general relativity. () gravity is actually a family of theories, each one defined by a different function, , of the Ricci scalar, . The simplest case is just the function bein ...
,
scalar–tensor theories such as
galileon theories,
brane cosmologies, the
DGP model The DGP model is a model of gravity proposed by Gia Dvali, Gregory Gabadadze, and Massimo Porrati in 2000. The model is popular among some model builders, but has resisted being embedded into string theory.
Overview
The DGP model assumes the exi ...
, and
massive gravity
In theoretical physics, massive gravity is a theory of gravity that modifies general relativity by endowing the graviton with a nonzero mass. In the classical theory, this means that gravitational waves obey a massive wave equation and hence travel ...
and its extensions such as
bimetric gravity
Bimetric gravity or bigravity refers to two different classes of theories. The first class of theories relies on modified mathematical theories of gravity (or gravitation) in which two metric tensors are used instead of one.
The second metric may ...
.
Successes
In addition to explaining many pre-2000 observations, the model has made a number of successful predictions: notably the existence of the
baryon acoustic oscillation
In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe, caused by Acoustics, acoustic density waves in the primordial plasma of the early universe. In the ...
feature, discovered in 2005 in the predicted location; and the statistics of weak
gravitational lensing
A gravitational lens is a distribution of matter (such as a galaxy cluster, cluster of galaxies) between a distant light source and an observer that is capable of bending the light from the source as the light travels toward the observer. This ...
, first observed in 2000 by several teams. The
polarization of the CMB, discovered in 2002 by DASI, has been successfully predicted by the model: in the 2015 ''Planck'' data release, there are seven observed peaks in the temperature (TT) power spectrum, six peaks in the temperature–polarization (TE) cross spectrum, and five peaks in the polarization (EE) spectrum. The six free parameters can be well constrained by the TT spectrum alone, and then the TE and EE spectra can be predicted theoretically to few-percent precision with no further adjustments allowed.
Challenges
Over the years, numerous simulations of ΛCDM and observations of our universe have been made that challenge the validity of the ΛCDM model, to the point where some cosmologists now believe that the ΛCDM model may be superseded by another standard cosmological model.
Lack of detection
Extensive searches for dark matter particles have so far shown no well-agreed detection; the dark energy may be almost impossible to detect in a laboratory, and its value is
unnaturally small compared to
vacuum energy theoretical predictions.
Violations of the cosmological principle
The ΛCDM model has been shown to satisfy the
cosmological principle
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throu ...
, which states that, on a large-enough scale, the universe looks the same in all directions (
isotropy
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
) and from every location (
homogeneity
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
); "the universe looks the same whoever and wherever you are." The cosmological principle exists because when the predecessors of the ΛCDM model were first being developed, there wasn't sufficient data available to distinguish between more complex anisotropic or inhomogeneous models, so homogeneity and isotropy were assumed to simplify the models, and the assumptions were carried over into the ΛCDM model.
However, recent findings have suggested that violations of the cosmological principle, especially of isotropy, exist. These violations have called the ΛCDM model into question, with some authors suggesting that the cosmological principle is now obsolete or that the
Friedmann–Lemaître–Robertson–Walker metric
The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
breaks down in the late universe.
This has additional implications for the validity of the
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
in the ΛCDM model, as
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
is implied by observations only if the cosmological principle is true.
Violations of isotropy
Evidence from
galaxy cluster
A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-l ...
s,
quasar
A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...
s, and
type Ia supernova
A Type Ia supernova (read: "type one-A") is a type of supernova that occurs in binary systems (two stars orbiting one another) in which one of the stars is a white dwarf. The other star can be anything from a giant star to an even smaller white ...
e suggest that isotropy is violated on large scales.
Data from the
Planck Mission
''Planck'' was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013, which mapped the anisotropies of the cosmic microwave background (CMB) at microwave and infrared frequencies, with high sensitivity and small angu ...
shows hemispheric bias in the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
in two respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The
European Space Agency
, owners =
, headquarters = Paris, Île-de-France, France
, coordinates =
, spaceport = Guiana Space Centre
, seal = File:ESA emblem seal.png
, seal_size = 130px
, image = Views in the Main Control Room (1205 ...
(the governing body of the Planck Mission) has concluded that these anisotropies in the CMB are, in fact, statistically significant and can no longer be ignored.
Already in 1967,
Dennis Sciama
Dennis William Siahou Sciama, (; 18 November 1926 – 18/19 December 1999) was a British physicist who, through his own work and that of his students, played a major role in developing British physics after the Second World War. He was the PhD ...
predicted that the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
has a significant dipole anisotropy.
In recent years, the CMB dipole has been tested, and current results suggest our motion with respect to distant radio galaxies and quasars differs from our motion with respect to the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
. The same conclusion has been reached in recent studies of the
Hubble diagram
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
of
Type Ia supernovae
A Type Ia supernova (read: "type one-A") is a type of supernova that occurs in binary systems (two stars orbiting one another) in which one of the stars is a white dwarf. The other star can be anything from a giant star to an even smaller white ...
and
quasars
A quasar is an extremely luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a mass ranging ...
. This contradicts the cosmological principle.
The CMB dipole is hinted at through a number of other observations. First, even within the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
, there are curious directional alignments and an anomalous parity asymmetry that may have an origin in the CMB dipole. Separately, the CMB dipole direction has emerged as a preferred direction in studies of alignments in quasar polarizations, scaling relations in galaxy clusters,
strong lensing
Strong gravitational lensing is a gravitational lensing effect that is strong enough to produce multiple images, arcs, or even Einstein rings. Generally, the strong lensing effect requires the projected lens mass density greater than the '' cri ...
time delay,
Type Ia supernovae, and quasars &
gamma-ray bursts
In gamma-ray astronomy, gamma-ray bursts (GRBs) are immensely energetic explosions that have been observed in distant galaxies. They are the most energetic and luminous electromagnetic events since the Big Bang. Bursts can last from ten millise ...
as
standard candles. The fact that all these independent observables, based on different physics, are tracking the CMB dipole direction suggests that the Universe is anisotropic in the direction of the CMB dipole.
Nevertheless, some authors have stated that the universe around Earth is isotropic at high significance by studies of the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
temperature maps.
Violations of homogeneity
Based on
N-body simulation
In physics and astronomy, an ''N''-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see ''n''-body problem for other applications). ''N''-body simulations ar ...
s in ΛCDM, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260
/h Mpc or more.
However, many large-scale structures have been discovered, and some authors have reported some of the structures to be in conflict with the predicted scale of homogeneity for ΛCDM, including
* The
Clowes–Campusano LQG
The Clowes–Campusano LQG (CCLQG; also called LQG 3 and U1.28) is a large quasar group, consisting of 34 quasars and measuring about 2 billion light-years across. It is one of the largest known superstructures in the observable universe. It is l ...
, discovered in 1991, which has a length of 580 Mpc
* The
Sloan Great Wall
The Sloan Great Wall (SGW) is a cosmic structure formed by a giant wall of galaxies (a galaxy filament). Its discovery was announced from Princeton University on October 20, 2003, by J. Richard Gott III, Mario Jurić, and their colleagues, b ...
, discovered in 2003, which has a length of 423 Mpc,
*
U1.11
U1.11 is a large quasar group located in the constellations of Leo and Virgo. It is one of the largest LQG's known, with the estimated maximum diameter of 780 Mpc (2.2 billion light-years) and contains 38 quasars. It was discovered in 2011 d ...
, a
large quasar group
A large quasar group (LQG) is a collection of quasars (a form of supermassive black hole active galactic nuclei) that form what are thought to constitute the largest astronomical structures in the observable universe. LQGs are thought to be prec ...
discovered in 2011, which has a length of 780 Mpc
* The
Huge-LQG
The Huge Large Quasar Group, (Huge-LQG, also called U1.27) is a possible structure or pseudo-structure of 73 quasars, referred to as a large quasar group, that measures about 4 billion light-years across. At its discovery, it was identified as ...
, discovered in 2012, which is three times longer than and twice as wide as is predicted possible according to ΛCDM
* The
Hercules–Corona Borealis Great Wall
The Hercules–Corona Borealis Great Wall or simply the Great Wall is the largest known structure in the observable universe, measuring approximately 10 billion light-years in length (the observable universe is about 93 billion light-years in di ...
, discovered in November 2013, which has a length of 2000–3000 Mpc (more than seven times that of the SGW)
*The
Giant Arc, discovered in June 2021, which has a length of 1000 Mpc
Other authors claim that the existence of structures larger than the scale of homogeneity in the ΛCDM model does not necessarily violate the cosmological principle in the ΛCDM model.
El Gordo galaxy cluster collision
El Gordo is an interacting galaxy cluster in the early Universe (
). The extreme properties of
El Gordo in terms of its redshift, mass, and the collision velocity leads to strong (
) tension with the ΛCDM model.
The properties of
El Gordo are however consistent with cosmological simulations in the framework of
MOND
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining ...
due to more rapid structure formation.
KBC void
The
KBC void
The KBC Void (or Local Hole) is an immense, comparatively empty region of space, named after astronomers Ryan Keenan, Amy Barger, and Lennox Cowie, who studied it in 2013. The existence of a local underdensity has been the subject of many pieces o ...
is an immense, comparatively empty region of space containing the
Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
approximately 2 billion light-years (600 megaparsecs, Mpc) in diameter.
Some authors have said the existence of the KBC void violates the assumption that the CMB reflects baryonic density fluctuations at
or Einstein's theory of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, either of which would violate the ΛCDM model,
while other authors have claimed that supervoids as large as the KBC void are consistent with the ΛCDM model.
Hubble tension
The
Hubble tension
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
in cosmology is widely acknowledged to be a major problem for the ΛCDM model.
In December 2021, ''
National Geographic
''National Geographic'' (formerly the ''National Geographic Magazine'', sometimes branded as NAT GEO) is a popular American monthly magazine published by National Geographic Partners. Known for its photojournalism, it is one of the most widely ...
'' reported that the cause of the Hubble tension discrepancy is not known. However, if the cosmological principle fails (see
Violations of the cosmological principle), then the existing interpretations of the Hubble constant and the Hubble tension have to be revised, which might resolve the Hubble tension.
Some authors postulate that the Hubble tension can be explained entirely by the
KBC void
The KBC Void (or Local Hole) is an immense, comparatively empty region of space, named after astronomers Ryan Keenan, Amy Barger, and Lennox Cowie, who studied it in 2013. The existence of a local underdensity has been the subject of many pieces o ...
, as measuring galactic
supernovae
A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or when a ...
inside a void is predicted by the authors to yield a larger local value for the Hubble constant than cosmological measures of the Hubble constant. However, other work has found no evidence for this in observations, finding the scale of the claimed underdensity to be incompatible with observations which extend beyond its radius. Important deficiencies were subsequently pointed out in this analysis, leaving open the possibility that the Hubble tension is indeed caused by outflow from the KBC void.
As a result of the Hubble tension, other researchers have called for new physics beyond the ΛCDM model.
Moritz Haslbauer et al. proposed that
MOND
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining ...
would resolve the Hubble tension.
Another group of researchers led by
Marc Kamionkowski
Marc Kamionkowski (born 1965) is an American theoretical physicist and currently the William R. Kenan, Jr. Professor of Physics and Astronomy at Johns Hopkins University. His research interests include particle physics, dark matter, inflation (c ...
proposed a cosmological model with early dark energy to replace ΛCDM.
S8 tension
The
tension in cosmology is another major problem for the ΛCDM model.
The
parameter in the ΛCDM model quantifies the amplitude of matter fluctuations in the late universe and is defined as
Early- (e.g. from CMB data collected using the Planck observatory) and late-time (e.g. measuring weak gravitational lensing events) facilitate increasingly precise values of
. However, these two categories of measurement differ by more standard deviations than their uncertainties. This discrepancy is called the
tension. The name "tension" reflects that the disagreement is not merely between two data sets: the many sets of early- and late-time measurements agree well within their own categories, but there is an unexplained difference between values obtained from different points in the evolution of the universe. Such a tension indicates that the ΛCDM model may be incomplete or in need of correction.
Axis of evil
The ΛCDM model assumes that the data of the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
and our interpretation of the CMB are correct. However, there exists an apparent correlation between the plane of the
Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
,
the rotation of
galaxies
A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...
, and certain aspects of the CMB. This may indicate that there is something wrong with the data or the interpretation of the cosmic microwave background used as evidence for the ΛCDM model, or that the
Copernican principle
In physical cosmology, the Copernican principle states that humans, on the Earth or in the Solar System, are not privileged observers of the universe, that observations from the Earth are representative of observations from the average position ...
and
cosmological principle
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throu ...
are violated.
Cosmological lithium problem
The actual observable amount of lithium in the universe is less than the calculated amount from the ΛCDM model by a factor of 3–4.
If every calculation is correct, then solutions beyond the existing ΛCDM model might be needed.
Shape of the universe
The ΛCDM model assumes that the
shape of the universe
The shape of the universe, in physical cosmology, is the local and global geometry of the universe. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes gen ...
is flat (zero curvature). However, recent Planck data have hinted that the shape of the universe might in fact be closed (positive curvature), which would contradict the ΛCDM model.
Some authors have suggested that the Planck data detecting a positive curvature could be evidence of a local inhomogeneity in the curvature of the universe rather than the universe actually being closed.
Violations of the strong equivalence principle
The ΛCDM model assumes that the
strong equivalence principle
In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
is true. However, in 2020 a group of astronomers analyzed data from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample, together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. They concluded that there was highly statistically significant evidence of violations of the strong equivalence principle in weak gravitational fields in the vicinity of rotationally supported galaxies. They observed an effect inconsistent with
tidal effects in the ΛCDM model.
Cold dark matter discrepancies
Several discrepancies between the predictions of
cold dark matter
In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a sm ...
in the ΛCDM model and observations of galaxies and their clustering have arisen. Some of these problems have proposed solutions, but it remains unclear whether they can be solved without abandoning the ΛCDM model.
Cuspy halo problem
The density distributions of dark matter halos in cold dark matter simulations (at least those that do not include the impact of baryonic feedback) are much more peaked than what is observed in galaxies by investigating their rotation curves.
Dwarf galaxy problem
Cold dark matter simulations predict large numbers of small dark matter halos, more numerous than the number of small dwarf galaxies that are observed around galaxies like the
Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
.
Satellite disk problem
Dwarf galaxies around the
Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
and
Andromeda galaxies are observed to be orbiting in thin, planar structures whereas the simulations predict that they should be distributed randomly about their parent galaxies.
High-velocity galaxy problem
Galaxies in the
NGC 3109
NGC 3109 is a small barred Magellanic type spiral or irregular galaxy around 4.34 Mly away in the direction of the constellation of Hydra. NGC 3109 is believed to be tidally interacting with the dwarf elliptical galaxy Antlia Dwarf. It was di ...
association are moving away too rapidly to be consistent with expectations in the ΛCDM model. In this framework,
NGC 3109
NGC 3109 is a small barred Magellanic type spiral or irregular galaxy around 4.34 Mly away in the direction of the constellation of Hydra. NGC 3109 is believed to be tidally interacting with the dwarf elliptical galaxy Antlia Dwarf. It was di ...
is too massive and distant from the
Local Group
The Local Group is the galaxy group that includes the Milky Way.
It has a total diameter of roughly , and a total mass of the order of .
It consists of two collections of galaxies in a "dumbbell" shape: the Milky Way and its satellites form ...
for it to have been flung out in a three-body interaction involving the
Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
or
Andromeda Galaxy
The Andromeda Galaxy (IPA: ), also known as Messier 31, M31, or NGC 224 and originally the Andromeda Nebula, is a barred spiral galaxy with the diameter of about approximately from Earth and the nearest large galaxy to the Milky Way. The gala ...
.
Galaxy morphology problem
If galaxies grew hierarchically, then massive galaxies required many mergers.
Major mergers inevitably create a classical
bulge
__NOTOC__
Bulge may refer to:
Astronomy and geography
*Bulge (astronomy), a tightly packed group of stars at the center of a spiral galaxy
*Equatorial bulge, a bulge around the equator of a planet due to rotation
* Tharsis bulge, vast volcanic pl ...
. On the contrary, about 80% of observed galaxies give evidence of no such bulges, and giant pure-disc galaxies are commonplace.
The tension can be quantified by comparing the observed distribution of galaxy shapes today with predictions from high-resolution hydrodynamical cosmological simulations in the ΛCDM framework, revealing a highly significant problem that is unlikely to be solved by improving the resolution of the simulations.
The high bulgeless fraction was nearly constant for 8 billion years.
Fast galaxy bar problem
If galaxies were embedded within massive halos of
cold dark matter
In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a sm ...
, then the bars that often develop in their central regions would be slowed down by
dynamical friction
In astrophysics, dynamical friction or Chandrasekhar friction, sometimes called ''gravitational drag'', is loss of momentum and kinetic energy of moving bodies through gravitational interactions with surrounding matter in space. It was first disc ...
with the halo. This is in serious tension with the fact that observed galaxy bars are typically fast.
Small scale crisis
Comparison of the model with observations may have some problems on sub-galaxy scales, possibly predicting
too many dwarf galaxies and too much dark matter in the innermost regions of galaxies. This problem is called the "small scale crisis". These small scales are harder to resolve in computer simulations, so it is not yet clear whether the problem is the simulations, non-standard properties of dark matter, or a more radical error in the model.
High redshift galaxies
Observations from the
James Webb Space Telescope
The James Webb Space Telescope (JWST) is a space telescope which conducts infrared astronomy. As the largest optical telescope in space, its high resolution and sensitivity allow it to view objects too old, distant, or faint for the Hubble Spa ...
have resulted in various galaxies confirmed by
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
at high redshift, such as
JADES-GS-z13-0
JADES-GS-z13-0 is a high-redshift Lyman-break galaxy discovered by the James Webb Space Telescope (JWST) during NIRCam imaging for the JWST Advanced Deep Extragalactic Survey (JADES) on 29 September 2022. Spectroscopic observations by JWST's ...
at
cosmological redshift
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
of 13.2.
Other candidate galaxies which have not been confirmed by spectroscopy include
CEERS-93316
CEERS-93316 is a candidate high-redshift galaxy, with an estimated redshift of approximately z = 16.4, corresponding to 236 million years after the Big Bang.
If confirmed, it would be one of the earliest and most distant known galaxies observe ...
at cosmological redshift of 16.7. Such a high rate of large galaxy formation in the early universe appears to contradict the rates of galaxy formation allowed in the existing Lambda CDM model via dark matter halos, as even if galaxy formation were 100% efficient and all mass were allowed to turn into stars in Lambda CDM, it wouldn't be enough to create such large galaxies.
Missing baryon problem
Massimo Persic and Paolo Salucci first estimated the baryonic density today present in ellipticals, spirals, groups and clusters of galaxies.
They performed an integration of the baryonic mass-to-light ratio over luminosity (in the following
), weighted with the luminosity function
over the previously mentioned classes of astrophysical objects:
:
The result was:
:
where
.
Note that this value is much lower than the prediction of standard cosmic nucleosynthesis
, so that stars and gas in galaxies and in galaxy groups and clusters account for less than 10% of the primordially synthesized baryons. This issue is known as the problem of the "missing baryons".
The missing baryon problem is claimed to be resolved. Using observations of the kinematic
Sunyaev–Zel'dovich effect spanning more than 90% of the lifetime of the Universe, in 2021 astrophysicists found that approximately 50% of all baryonic matter is outside
dark matter halo
According to modern models of physical cosmology, a dark matter halo is a basic unit of cosmological structure. It is a hypothetical region that has decoupled from cosmic expansion and contains gravitationally bound matter.
A single dark matte ...
es, filling the space between galaxies. Together with the amount of baryons inside galaxies and surrounding these, the total amount of baryons in the late time Universe is now compatible with early Universe measurements.
Unfalsifiability
It has been argued that the ΛCDM model is built upon a foundation of
conventionalist stratagems, rendering it
unfalsifiable
Falsifiability is a standard of evaluation of scientific theories and hypotheses that was introduced by the philosopher of science Karl Popper in his book ''The Logic of Scientific Discovery'' (1934). He proposed it as the cornerstone of a so ...
in the sense defined by
Karl Popper
Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian-British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the cl ...
.
Parameters
The simple ΛCDM model is based on six
parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
s: physical baryon density parameter; physical dark matter density parameter; the age of the universe; scalar spectral index; curvature fluctuation amplitude; and reionization optical depth.
In accordance with
Occam's razor
Occam's razor, Ockham's razor, or Ocham's razor ( la, novacula Occami), also known as the principle of parsimony or the law of parsimony ( la, lex parsimoniae), is the problem-solving principle that "entities should not be multiplied beyond neces ...
, six is the smallest number of parameters needed to give an acceptable fit to current observations; other possible parameters are fixed at "natural" values, e.g. total density parameter = 1.00, dark energy equation of state = −1. (See below for extended models that allow these to vary.)
The values of these six parameters are mostly not predicted by current theory (though, ideally, they may be related by a future "
Theory of Everything
A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all asp ...
"), except that most versions of
cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity ...
predict the scalar spectral index should be slightly smaller than 1, consistent with the estimated value 0.96. The parameter values, and uncertainties, are estimated using large computer searches to locate the region of parameter space providing an acceptable match to cosmological observations. From these six parameters, the other model values, such as the
Hubble constant
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
and the
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
density, can be readily calculated.
Commonly, the set of observations fitted includes the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
anisotropy, the brightness/redshift relation for supernovae, and large-scale galaxy clustering including the
baryon acoustic oscillation
In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe, caused by Acoustics, acoustic density waves in the primordial plasma of the early universe. In the ...
feature. Other observations, such as the Hubble constant, the abundance of galaxy clusters,
weak gravitational lensing
While the presence of any mass bends the path of light passing near it, this effect rarely produces the giant arcs and multiple images associated with strong gravitational lensing. Most lines of sight in the universe are thoroughly in the weak l ...
and globular cluster ages, are generally consistent with these, providing a check of the model, but are less precisely measured at present.
Parameter values listed below are from the ''Planck'' Collaboration Cosmological parameters 68% confidence limits for the base ΛCDM model from ''Planck'' CMB power spectra, in combination with lensing reconstruction and external data (BAO + JLA + H
0).
See also
Planck (spacecraft)
''Planck'' was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013, which mapped the anisotropies of the cosmic microwave background (CMB) at microwave and infrared frequencies, with high sensitivity and small angu ...
.
Extended models
Extended models allow one or more of the "fixed" parameters above to vary, in addition to the basic six; so these models join smoothly to the basic six-parameter model in the limit that the additional parameter(s) approach the default values. For example, possible extensions of the simplest ΛCDM model allow for spatial curvature (
may be different from 1); or
quintessence rather than a
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
where the
equation of state
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal ...
of dark energy is allowed to differ from −1. Cosmic inflation predicts tensor fluctuations (
gravitational wave
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...
s). Their amplitude is parameterized by the tensor-to-scalar ratio (denoted
), which is determined by the unknown energy scale of inflation. Other modifications allow
hot dark matter
Hot dark matter (HDM) is a theoretical form of dark matter which consists of particles that travel with ultrarelativistic velocities.
Dark matter is a form of matter that neither emits nor absorbs light. Within physics, this behavior is character ...
in the form of
neutrino
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
s more massive than the minimal value, or a running spectral index; the latter is generally not favoured by simple cosmic inflation models.
Allowing additional variable parameter(s) will generally ''increase'' the uncertainties in the standard six parameters quoted above, and may also shift the central values slightly. The Table below shows results for each of the possible "6+1" scenarios with one additional variable parameter; this indicates that, as of 2015, there is no convincing evidence that any additional parameter is different from its default value.
Some researchers have suggested that there is a running spectral index, but no statistically significant study has revealed one. Theoretical expectations suggest that the tensor-to-scalar ratio
should be between 0 and 0.3, and the latest results are now within those limits.
See also
*
Bolshoi Cosmological Simulation
The Bolshoi simulation, a computer model of the universe run in 2010 on the Pleiades supercomputer at the NASA Ames Research Center, was the most accurate cosmological simulation to that date of the evolution of the large-scale structure of the u ...
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Galaxy formation and evolution
The study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous universe from a homogeneous beginning, the formation of the first galaxies, the way galaxies change over time, and the processes that have ge ...
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Illustris project
The Illustris project was a series of astrophysical simulations run by an international collaboration of scientists. The aim was to study the processes of galaxy formation and evolution in the universe with a comprehensive physical model. Early r ...
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List of cosmological computation software
The cosmic microwave background (CMB) is the thermal radiation assumed to be left over from the " Big Bang" of cosmology. The CMB is a snapshot of the oldest light in our universe, imprinted on the sky when the universe was just 380,000 years ol ...
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Millennium Run
The Millennium Run, or Millennium Simulation (referring to its size
) is a computer N-body simulation used to investigate how the distribution of matter in the Universe has evolved over time, in particular, how the observed population of galaxies ...
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Weakly interacting massive particles
Weakly interacting massive particles (WIMPs) are hypothetical particles that are one of the proposed candidates for dark matter.
There exists no formal definition of a WIMP, but broadly, a WIMP is a new elementary particle which interacts via gra ...
(WIMPs)
* The ΛCDM model is also known as the standard model of cosmology, but is not related to the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying a ...
of particle physics.
References
Further reading
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External links
Cosmology tutorial/NedWrightMillennium SimulationWMAP estimated cosmological parameters/Latest Summary
{{DEFAULTSORT:Lambda-Cdm Model
Physical cosmology
Dark matter
Dark energy
Concepts in astronomy
Scientific models