Primordial fluctuations

Primordial fluctuations are density variations in the early universe that are considered to be the origin of the structure of the universe. These variations are due to vacuum fluctuations and grew with rapid expansion during the inflation of the universe . It is believed that the universe was in thermodynamic equilibrium before inflation . Therefore, without these fluctuations, the universe would be completely homogeneous and no galaxies and galaxy clusters would have formed.

Observations of cosmic background radiation and redshift are used to measure the present and past distribution of matter. Properties of the primordial fluctuations can be extrapolated from these measurements. Since the fluctuations have probably increased with inflation, these measurements can constrain the parameters within the theory of inflation.

formalism

Primordial fluctuations are usually quantified with the spectral power density , which indicates the strength of the variations as a function of the spatial order of magnitude. Within this formalism, the relative fluctuation of the mass density is calculated with:

{\ displaystyle \ delta ({\ vec {x}}) \ equiv {\ frac {\ rho ({\ vec {x}})} {\ bar {\ rho}}} - 1 = \ sum _ {k} \ delta _ {k} e ^ {i {\ vec {k}} \ cdot {\ vec {x}}}}

${\ displaystyle {\ bar {\ rho}}}$ corresponds to the average mass density. Many inflation models predict that the fluctuations follow a power law in which

{\ displaystyle P_ {s} (k) \ propto k ^ {n}}

,

where the wave number of the fluctuations in Mpc is ⁻¹ and ${\ displaystyle k}$

{\ displaystyle P (k) \ equiv | \ delta _ {k} | ^ {2}}

.

For scalar fluctuations denotes the scalar index . The model with corresponds to scale-invariant fluctuations. ${\ displaystyle n + 1}$ ${\ displaystyle n = 0}$

Adiabatic fluctuations

Adiabatic fluctuations are density fluctuations of all forms of matter or energy , which are proportionally equally compressed. z. B. corresponds to an adiabatic compression of photons by a factor of 2 with a compression of electrons by the same factor. The density fluctuations for one component do not necessarily have to correspond to density fluctuations in other components. Although the fluctuations are believed to be adiabatic, recent measurements suggest that uncorrelated density fluctuations were present. However, uncorrelated dark matter vibrational modes are considered unlikely.

Tensor modes

The existence of tensor fluctuations (in the form of gravitational waves ) is predicted by many models of inflation. Like scalar fluctuations, tensor fluctuations obey a power law, with the tensor index (analogous to the scalar index) and the ratio of tensor to scalar power density as parameters.

literature

Patrick Crotty: Bounds on isocurvature perturbations from CMB and LSS data . In: Physical Review Letters (English) arxiv : astro-ph / 0306286 .
Andrei Linde : Quantum Cosmology and the Structure of Inflationary Universe . Invited talk (English) arxiv : gr-qc / 9508019 .
Hiranya Peiris: First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation . In: Astrophysical Journal (English) arxiv : astro-ph / 0302225 .
Max Tegmark: Cosmological parameters from SDSS and WMAP . In: Physical Review D (English) arxiv : astro-ph / 0310723 .