Primordial fluctuations

Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. These variations originated as quantum fluctuations, and grew from the rapid expansion which occurred during cosmic inflation. The observable universe is thought to have been in thermal equilibrium prior to inflation. Thus, without these fluctuations, the universe would be completely homogeneous, and galaxies and galaxy clusters would not have formed.

Observations of the cosmic microwave background and redshift surveys are used to measure the current and past distribution of matter. From these measurements, characteristics of the primordial fluctuations can be extrapolated. Since the fluctuations are believed to arise from inflation, such measurements can also set constraints on parameters within inflationary theory.

Contents

1 Formalism

2 Adiabatic/Isocurvature Fluctuations

3 Tensor Modes

4 See also

5 References and external links

Formalism

Primordial fluctuations are typically quantified by a power spectrum which gives the power of the variations as a function of spatial scale. Within this formalism, the fractional mass density of the fluctuations is given by:

$\delta(\vec{x}) \equiv \frac{\rho(\vec{x})}{\bar{\rho}} - 1 = \sum_k \delta_k e^{i\vec{k} \cdot \vec{x}}$

where $\bar{\rho}$ is the average mass density. Many inflationary models predict the fluctuations obey a power law in which

Failed to parse (unknown function \propto): P_s(k) \propto k^n

where $k$ is the wavenumber of the fluctuations in Mpc⁻¹ and

$P(k) \equiv |\delta_k|^2$ .

For scalar fluctuations, $n + 1$ is referred to as the scalar index. The $n = 0$ model corresponds to scale invariant fluctuations.

Adiabatic/Isocurvature Fluctuations

Adiabatic fluctuations are density variations in all forms of matter and energy which have equal fractional over/under densities. So for example, an adiabatic photon overdensity of a factor of two would also correspond to a electron overdensity of two. For isocurvature fluctuations, the density variations for one component do not necessarily correspond to density variations in other components. While it is usually assumed that the initial flucuations are adiabatic, the possibility of isocurvature fluctuations can be considered given current cosmological data. While the overall constraints are inconclusive, uncorrelated isocurvature cold dark matter modes are found to be unlikely.

Tensor Modes

The presence of primordial tensor fluctuations (manifested as gravity waves) 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), and the ratio of the tensor to scalar power.

References and 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.

Categories: Cosmology