Relativistic effects and primordial non-Gaussianity in the matter density fluctuation

TL;DR

This paper derives a third-order analytic solution for matter density fluctuations in a relativistic framework, clarifying the influence of primordial non-Gaussianity and relativistic effects on structure formation.

Contribution

It provides the first third-order relativistic solution for matter density fluctuations in the proper-time hypersurface, connecting local Newtonian and relativistic descriptions.

Findings

Relativistic effects vanish on large scales due to coordinate rescaling.

The initial curvature perturbation influences nonlinear evolution.

Effective non-Gaussian parameters are computed from relativistic nonlinearities.

Abstract

We present the third-order analytic solution of the matter density fluctuation in the proper-time hypersurface of nonrelativistic matter flows by solving the nonlinear general relativistic equations. The proper-time hypersurface provides a coordinate system that a local observer can set up without knowledge beyond its neighborhood, along with physical connections to the local Newtonian descriptions in the relativistic context. The initial condition of our analytic solution is set up by the curvature perturbation in the comoving gauge, clarifying its impact on the nonlinear evolution. We compute the effective non-Gaussian parameters due to the nonlinearity in the relativistic equations. With proper coordinate rescaling, we show that the equivalence principle is respected and the relativistic effect vanishes in the large-scale limit.