The exact analytical solution of the linear structure growth rate in LCDM cosmology and its cosmological applications

TL;DR

This paper derives an exact analytical solution for the linear structure growth rate in LCDM cosmology, incorporating relativistic corrections, and explores their implications for cosmological observations and simulations.

Contribution

It provides the first exact solution including all relativistic effects, valid at all scales, and assesses their impact on cosmological measurements and simulations.

Findings

Relativistic corrections alter density growth by 10% from z=100 to z=0 at certain scales.

These corrections introduce a scale dependence mimicking local-type primordial non-Gaussianity.

A post-processing recipe is provided to correct for relativistic effects in large-scale simulations.

Abstract

We derive the exact analytical solution of the linear structure growth rate in LCDM cosmology with flat or curved geometry, under the Newtonian gauge. Unlike the well known solution under the Newtonian limit (Heath 1977), our solution takes all general relativistic corrections into account and is hence valid at both the sub- and super-horizon scales. With this exact solution, we evaluate cosmological impacts induced by these relativistic corrections. (1) General relativistic corrections alter the density growth from z=100 to z=0 by 10% at k=0.01h/Mpc and the impact becomes stronger toward larger scales. We caution the readers that the overdensity is not gauge invariant and the above statement is restrained to the Newtonian gauge. (2) Relativistic corrections introduce a k^{-2} scale dependence in the density fluctuation. It mimics a primordial non-Gaussianity of the local type with $f^{\rm local}_{\rm NL}\sim 1$. This systematical error may become non-negligible for future all sky deep galaxy surveys. (3) Cosmological simulations with box size greater than 1Gpc are also affected by these relativistic corrections. We provide a post-processing recipe to correct for these effects. (4) These relativistic corrections affect the redshift distortion. However, at redshifts and scales relevant to redshift distortion measurements, such effect is negligible.