Primordial fluctuations are
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
variations in the early universe which are considered the seeds of all
structure
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...
in the universe. Currently, the most widely accepted explanation for their origin is in the context 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 ...
. According to the inflationary paradigm, the exponential growth of the
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 ...
during inflation caused
quantum fluctuation
In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. ...
s of the inflation field to be stretched to macroscopic scales, and, upon leaving the
horizon
The horizon is the apparent line that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This line divides all viewing directions based on whether i ...
, to "freeze in".
At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the
initial conditions
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted ''t'' = 0). For ...
for
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 ...
.
The statistical properties of the primordial fluctuations can be inferred from observations of
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
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 from measurements of the distribution of matter, e.g., galaxy
redshift survey
In astronomy, a redshift survey is a survey of a section of the sky to measure the redshift of astronomical objects: usually galaxies, but sometimes other objects such as galaxy clusters or quasars.
Using Hubble's law, the redshift can be used ...
s. Since the fluctuations are believed to arise from inflation, such measurements can also set constraints on parameters within inflationary theory.
Formalism
Primordial fluctuations are typically quantified by a
power spectrum
The power spectrum S_(f) of a time series x(t) describes the distribution of Power (physics), power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discre ...
which gives the power of the variations as a function of spatial scale. Within this formalism, one usually considers the fractional energy density of the fluctuations, given by:
:
where
is the energy density,
its average and
the
wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the ''spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temp ...
of the fluctuations. The power spectrum
can then be defined via the ensemble average of the
Fourier components:
:
There are both scalar and tensor modes of fluctuations.
Scalar modes
Scalar modes have the power spectrum
:
Many inflationary models predict that the scalar component of the fluctuations obeys a
power law
In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, inde ...
in which
:
For scalar fluctuations,
is referred to as the scalar spectral index, with
corresponding to
scale invariant
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality.
The technical term ...
fluctuations.
The scalar ''spectral index'' describes how the density fluctuations vary with scale. As the size of these fluctuations depends upon the inflaton's motion when these quantum fluctuations are becoming super-horizon sized, different inflationary potentials predict different spectral indices. These depend upon the slow roll parameters, in particular the gradient and curvature of the potential. In models where the curvature is large and positive
. On the other hand, models such as monomial potentials predict a red spectral index
. Planck provides a value of
of 0.96.
Tensor modes
The presence of primordial
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
fluctuations is predicted by many inflationary models. As with scalar fluctuations, tensor fluctuations are expected to follow a power law and are parameterized by the tensor index (the tensor version of the scalar index). The ratio of the tensor to scalar power spectra is given by
:
where the 2 arises due to the two polarizations of the tensor modes. 2015
CMB data from the
Planck satellite
''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 ...
gives a constraint of
.
Adiabatic/isocurvature fluctuations
Adiabatic fluctuations are density variations in all forms of
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 ...
and
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
which have equal fractional over/under densities in the number density. So for example, an adiabatic
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 ...
overdensity of a factor of two in the number density would also correspond to an
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
overdensity of two. For isocurvature fluctuations, the number density variations for one component do not necessarily correspond to number density variations in other components. While it is usually assumed that the initial fluctuations are adiabatic, the possibility of isocurvature fluctuations can be considered given current cosmological data. Current
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 ...
data favor adiabatic fluctuations and constrain uncorrelated isocurvature
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 ...
modes to be small.
See also
*
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 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 ...
*
Cosmic microwave background spectral distortions
CMB spectral distortions are tiny departures of the average cosmic microwave background (CMB) frequency spectrum from the predictions given by a perfect black body. They can be produced by a number of standard and non-standard processes occurring ...
*
Press–Schechter formalism
The Press–Schechter formalism is a mathematical model for predicting the number of objects (such as galaxies, galaxy clusters or dark matter halos) of a certain mass within a given volume of the Universe. It was described in an academic paper by ...
*
Primordial gravitational wave
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 space ...
*
Primordial black hole
Primordial black holes (also abbreviated as PBH) are hypothetical black holes that formed soon after the Big Bang. Due to the extreme environment of the newly born universe, extremely dense pockets of sub-atomic matter had been tightly packed to ...
References
External links
* Crotty, Patrick, "Bounds on isocurvature perturbations from CMB and LSS data". Physical Review Letters.
* Linde, Andrei, "Quantum Cosmology and the Structure of Inflationary Universe". Invited talk.
*
Peiris, Hiranya, "First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation". Astrophysical Journal.
* Tegmark, Max, "Cosmological parameters from SDSS and WMAP". Physical Review D. {{arxiv, astro-ph/0310723
Physical cosmology
Inflation (cosmology)