An inhomogeneous cosmology is a physical
cosmological theory (an astronomical model of the physical
universe's origin and evolution) which, unlike the currently widely accepted
cosmological concordance model, assumes that inhomogeneities in the
distribution of matter across the universe affect local
gravitational forces (i.e., at the galactic level) enough to skew our view of the Universe.
When the universe began, matter was distributed
homogeneous
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 ...
ly, but over billions of years,
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. ...
,
clusters of galaxies
The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these obj ...
, and
supercluster
A supercluster is a large group of smaller galaxy clusters or galaxy groups; they are among the largest known structures in the universe. The Milky Way is part of the Local Group galaxy group (which contains more than 54 galaxies), which in turn ...
s have coalesced, and must, according to
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 ...
, warp the
space-time
In physics, spacetime is a mathematical model that combines the three-dimensional space, three dimensions of space and one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visualize S ...
around them. While the concordance model acknowledges this fact, it assumes that such inhomogeneities are not sufficient to affect large-scale averages of gravity in our observations. When two separate studies
claimed in 1998-1999 that high
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 ...
supernovae were further away than our calculations showed they should be, it was suggested that the
expansion of the universe
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...
is
accelerating
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by th ...
, and
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 ...
, a repulsive energy inherent in space, was proposed to explain the acceleration. Dark energy has since become widely accepted, but it remains unexplained. Accordingly, some scientists continue to work on models that might not require dark energy. Inhomogeneous cosmology falls into this class.
Inhomogeneous cosmologies assume that the
backreactions of denser structures, as well as those of very empty voids, on
space-time
In physics, spacetime is a mathematical model that combines the three-dimensional space, three dimensions of space and one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visualize S ...
are significant enough that when not taken into account, they distort our understanding of time and our observations of distant objects. Following
Thomas Buchert's publication of equations in 1997 and 2000 that derive from general relativity but also allow for the inclusion of local gravitational variations, a number of cosmological models were proposed under which the acceleration of the universe is in fact a misinterpretation of our astronomical observations and in which dark energy is unnecessary to explain them. For example, in 2007, David Wiltshire proposed a model (timescape cosmology) in which backreactions have caused
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
to run more slowly or, in
voids
Void may refer to:
Science, engineering, and technology
* Void (astronomy), the spaces between galaxy filaments that contain no galaxies
* Void (composites), a pore that remains unoccupied in a composite material
* Void, synonym for vacuum, a s ...
, more quickly, thus giving the supernovae observed in 1998 the illusion of being further away than they were.
Timescape cosmology may also imply that the expansion of the universe is in fact slowing.
History
Standard cosmological model
The conflict between the two cosmologies derives from the inflexibility of
Einstein's theory of general relativity, which shows how gravity is formed by the interaction of matter, space, and time.
Physicist
John Wheeler famously summed up the theory's essence as "Matter tells space how to curve; space tells matter how to move."
However, in order to build a workable cosmological model, all of the terms on both sides of Einstein's equations must be balanced: on one side, matter (i.e., all the things that warp time and space); on the other, 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 ...
of the universe and the speed at which space-time is expanding.
In short, a model requires a particular amount of matter in order to produce particular curvatures and expansion rates.
In terms of matter, all modern cosmologies are founded on 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 whichever direction we look from earth, the universe is basically the same: homogeneous and
isotropic
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 ...
(uniform in all dimensions).
This principle grew out of Copernicus's assertion that there were no special observers in the universe and nothing special about the earth's location in the universe (i.e., Earth was not the center of the universe, as previously thought). Since the publication of general relativity in 1915, this homogeneity and isotropy have greatly simplified the process of devising cosmological models.
![End_of_universe](https://upload.wikimedia.org/wikipedia/commons/9/98/End_of_universe.jpg)
In terms of the curvature of space-time and the
shape of the universe, it can theoretically be closed (positive curvature, or space-time folding in itself as though on a
four-dimensional
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', ...
sphere's surface), open (negative curvature, with space-time folding outward), or flat (zero curvature, like the surface of a "flat" four-dimensional piece of paper).
The first real difficulty came with regards to expansion, for in 1905, as previously, the universe was assumed to be static, neither expanding nor contracting. All of Einstein's solutions to his equations in general relativity, however, predicted a dynamic universe. Therefore, in order to make his equations consistent with the apparently static universe, he added 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 eq ...
, a term representing some unexplained extra energy. But when in the late 1920s
Georges Lemaître's and
Edwin Hubble's observations proved
Alexander Friedmann's notion (derived from general relativity) that the
universe was expanding, the cosmological constant became unnecessary, Einstein calling it "my greatest blunder."
With this term gone from the equation, others derived the
Friedmann-Lemaître–Robertson–Walker (FLRW) solution to describe such an expanding universe — a solution built on the assumption of a flat, isotropic, homogeneous universe. The FLRW model became the foundation of the standard model of a universe created by the Big Bang, and further observational evidence has helped to refine it. For example, a smooth, mostly homogeneous, and (at least when it was almost 400,000 years old) flat universe seemed to be confirmed by data from the
cosmic microwave background (CMB). And after galaxies and clusters of galaxies were found in the 1970s to be rotating faster than they should without flying apart, the existence of
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 ...
seemed also proven, confirming its inference by
Jacobus Kapteyn
Prof Jacobus Cornelius Kapteyn FRS FRSE LLD (19 January 1851 – 18 June 1922) was a Dutch astronomer. He carried out extensive studies of the Milky Way and was the discoverer of evidence for galactic rotation. Kapteyn was also among the fi ...
,
Jan Oort
Jan Hendrik Oort ( or ; 28 April 1900 – 5 November 1992) was a Dutch astronomer who made significant contributions to the understanding of the Milky Way and who was a pioneer in the field of radio astronomy. His ''New York Times'' obituary ...
, and
Fritz Zwicky
Fritz Zwicky (; ; February 14, 1898 – February 8, 1974) was a Swiss astronomer. He worked most of his life at the California Institute of Technology in the United States of America, where he made many important contributions in theoretical and ...
in the 1920s and 1930s and demonstrating the flexibility of the standard model. Dark matter is believed to make up roughly 23% of the energy density of the universe.
Dark energy
![CMB_Timeline75](https://upload.wikimedia.org/wikipedia/commons/6/60/CMB_Timeline75.jpg)
Another observation in 1998 seemed to complicate the situation further: two separate studies
found distant supernovae to be fainter than expected in a steadily expanding universe; that is, they were not merely moving away from the earth but accelerating. The universe's expansion was calculated to have been
accelerating
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by th ...
since approximately 5 billion years ago. Given the gravitation braking effect that all the matter of the universe should have had on this expansion, a variation of Einstein's cosmological constant was reintroduced to represent an energy inherent in space, balancing the equations for a flat, accelerating universe. It also gave Einstein's cosmological constant new meaning, for by reintroducing it into the equation to represent dark energy, a flat universe expanding ever faster can be reproduced.
Although the nature of this energy has yet to be adequately explained, it makes up almost 70% of the energy density of the universe in the concordance model. And thus, when including dark matter, almost 95% of the universe's energy density is explained by phenomena that have been inferred but not entirely explained nor directly observed. Most cosmologists still accept the concordance model, although science journalist Anil Ananthaswamy calls this agreement a "wobbly orthodoxy."
Inhomogeneous universe
![WMAP_image_of_the_CMB_anisotropy](https://upload.wikimedia.org/wikipedia/commons/c/c1/WMAP_image_of_the_CMB_anisotropy.jpg)
While the universe began with homogeneously distributed matter, enormous structures have since coalesced over billions of years: hundreds of billions of stars inside of galaxies, clusters of galaxies, superclusters, and vast
filaments of matter. These denser regions and the voids between them must, under general relativity, have some effect, as matter dictates how space-time curves. So the extra mass of galaxies and galaxy clusters (and dark matter, should particles of it ever be directly detected) must cause nearby space-time to curve more positively, and voids should have the opposite effect, causing space-time around them to take on negative curvatures. The question is whether these effects, called
backreactions, are negligible or together comprise enough to change the universe's geometry. Most scientists have assumed that they are negligible, but this has partly been because there has been no way to average space-time geometry in Einstein's equations.
In 2000, a set of new equations—now referred to as the set of
Buchert equations—based on general relativity was published by cosmologist Thomas Buchert of the
École Normale Supérieure
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
in Lyon, France, which allow the effects of a non-uniform distribution of matter to be taken into account but still allow the behavior of the universe to be averaged. Thus, models based on a lumpy, inhomogeneous distribution of matter could now be devised.
"There is no dark energy, as far as I'm concerned," Buchert told ''New Scientist'' in 2016. "In ten years' time, dark energy is gone." In the same article, cosmologist Syksy Räsänen said, "It’s not been established beyond reasonable doubt that dark energy exists. But I’d never say that it has been established that dark energy does not exist." He also told the magazine that the question of whether backreactions are negligible in cosmology "has not been satisfactorily answered."
Inhomogeneous cosmology
Inhomogeneous cosmology in the most general sense (assuming a totally inhomogeneous universe) is modeling the universe as a whole with the spacetime which does not possess any
spacetime symmetries
Spacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry. The role of symmetry in physics is important in simplifying solutions to many problems. Spacetime symmetries are used in the study of exact ...
. Typically considered cosmological spacetimes have either the maximal symmetry, which comprises three translational symmetries and three rotational symmetries (homogeneity and isotropy with respect to every point of spacetime), the translational symmetry only (homogeneous models), or the rotational symmetry only (spherically symmetric models). Models with less symmetries (e.g. axisymmetric) are also considered as symmetric. However, it is common to call spherically symmetric models or non-homogeneous models as inhomogeneous. In inhomogeneous cosmology, the large-scale structure of the universe is modeled by exact solutions of the Einstein field equations (i.e. non-perturbatively), unlike
cosmological perturbation theory
In physical cosmology, cosmological perturbation theory is the theory by which the ''evolution of structure'' is understood in the Big Bang model. It uses general relativity to compute the gravitational forces causing small perturbations to grow an ...
, which is study of the universe that takes
structure formation
In physical cosmology, structure formation is the formation of galaxies, galaxy clusters and larger structures from small early density fluctuations. The universe, as is now known from observations of the cosmic microwave background radiation, beg ...
(
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. ...
,
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, the
cosmic web
The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these obj ...
) into account but in a perturbative way.
[Krasinski, A., ''Inhomogeneous Cosmological Models'', (1997) Cambridge UP, ]
Inhomogeneous cosmology usually includes the study of structure in the Universe by means of exact solutions of
Einstein's 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 ...
(i.e. ''
metrics
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathema ...
'')
or by spatial or spacetime averaging methods.
Such models are not
homogeneous
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 ...
,
[Ryan, M.P., Shepley, L.C., ''Homogeneous Relativistic Cosmologies'', (1975) Princeton UP, ] but may allow effects which can be interpreted 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 ...
, or can lead to cosmological structures such as voids or galaxy clusters.
Perturbative approach
Perturbation theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle ...
, which deals with small perturbations from e.g. a homogeneous metric, only holds as long as the perturbations are not too large, and N-body simulations use Newtonian gravity which is only a good approximation when speeds are low and gravitational fields are weak.
Non-perturbative approach
Work towards a non-perturbative approach includes the Relativistic Zel'dovich Approximation.
, Thomas Buchert,
George Ellis,
Edward Kolb, and their colleagues
judged that if the universe is described by cosmic variables in a
backreaction
In theoretical physics, back-reaction (or backreaction) is often necessary to calculate the self-consistent behaviour of a particle or an object in an external field.
Intuitive definition
When a particle is considered to have no mass or to have a ...
scheme that includes
coarse-graining and averaging, then whether dark energy is an artifact of the traditional way of using the Einstein equation remains an unanswered question.
Exact solutions
The first historical examples of inhomogeneous (though spherically symmetric) solutions are the
Lemaître–Tolman metric
In physics, the Lemaître–Tolman metric, also known as the Lemaître–Tolman–Bondi metric or the Tolman metric, is a Lorentzian metric based on an exact solution of Einstein's field equations; it describes an isotropic and expanding (or co ...
(or LTB model - Lemaître–Tolman-Bondi
). The
Stephani metric can be spherically symmetric or totally inhomogeneous.
Other examples are the Szekeres metric, Szafron metric, Barnes metric, Kustaanheimo-Qvist metric, and Senovilla metric.
The Bianchi metrics as given in the
Bianchi classification In mathematics, the Bianchi classification provides a list of all real 3-dimensional Lie algebras ( up to isomorphism). The classification contains 11 classes, 9 of which contain a single Lie algebra and two of which contain a continuum-sized fam ...
and
Kantowski-Sachs metrics are homogeneous.
Averaging methods
The best-known averaging approach is the scalar averaging approach, leading to the kinematical
backreaction
In theoretical physics, back-reaction (or backreaction) is often necessary to calculate the self-consistent behaviour of a particle or an object in an external field.
Intuitive definition
When a particle is considered to have no mass or to have a ...
and mean 3-Ricci curvature functionals.
Buchert's equations are the main equations of such averaging methods.
Timescape cosmology
In 2007, David Wiltshire, a professor of theoretical physics at the
University of Canterbury
The University of Canterbury ( mi, Te Whare Wānanga o Waitaha; postnominal abbreviation ''Cantuar.'' or ''Cant.'' for ''Cantuariensis'', the Latin name for Canterbury) is a public research university based in Christchurch, New Zealand. It was ...
in New Zealand, argued in the ''New Journal of Physics'' that quasilocal variations in gravitational energy had in 1998 given the false conclusion that the expansion of the universe is accelerating.
Moreover, due to the
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 ...
, which holds that gravitational and inertial energy are equivalent and thus prevents aspects of gravitational energy from being differentiated at a local level, scientists thus misidentified these aspects 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 ...
.
This misidentification was the result of presuming an essentially homogeneous universe, as the standard cosmological model does, and not accounting for temporal differences between matter-dense areas and voids. Wiltshire and others argued that if the universe is not only assumed not to be homogeneous but also not flat, models could be devised in which the apparent acceleration of the universe's expansion could be explained otherwise.
One more important step being left out of the standard model, Wiltshire claimed, was the fact that as proven by observation, gravity slows time. Thus, from the perspective of the same observer, a clock will move faster in empty space, which possesses low gravitation, than inside a galaxy, which has much more gravity, and he argued that as large as a 38% difference between the time on clocks in the Milky Way and those in a galaxy floating in a void exists. Thus, unless we can correct for that—timescapes each with different times—our observations of the expansion of space will be, and are, incorrect. Wiltshire claims that the 1998 supernovae observations that led to the conclusion of an expanding universe and dark energy can instead be explained by Buchert's equations if certain strange aspects of general relativity are taken into account.
References
{{Reflist
External links
Inhomogeneous cosmology@ nlab
Physical cosmology
Dark energy