Quasi-isotropic solution of the Einstein equations near a cosmological singularity for a two-fluid cosmological model

TL;DR

This paper generalizes the quasi-isotropic solution of Einstein's equations near a cosmological singularity to a two-fluid model, describing large deviations from homogeneity while local measurements remain close to FRW values.

Contribution

It extends the Lifshitz-Khalatnikov quasi-isotropic solution to include two-fluid cosmological models with explicit calculations of the series expansion coefficients.

Findings

Describes non-decreasing scalar and gravitational wave perturbations.

Provides explicit first coefficients of the metric and fluid variables.

Shows large metric deviations can occur with near-FRW local measurements.

Abstract

The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized to the case of a two-fluid cosmological model. This solution describes non-decreasing modes of adiabatic and isocurvature scalar perturbations and gravitational waves in the regime when deviations of a space-time metric from the homogeneous isotropic Friedmann-Robertson-Walker (FRW) background are large while locally measurable quantities like Riemann tensor components are still close to their FRW values. The general structure of the perturbation series is presented and the first coefficients of the series expansion for the metric tensor and the fluid energy densities and velocities are calculated explicitly.