Nonlinear cosmological consistency relations and effective matter stresses

TL;DR

This paper develops a nonlinear covariant framework to test cosmological models using large-scale structure, revealing effective stresses at second order and their implications for interpreting cosmological observations.

Contribution

It introduces a covariant, metric-based nonlinear framework for cosmological consistency relations, extending first order conditions to second order and analyzing effective stresses in structure formation.

Findings

Effective pressures and anisotropic stresses appear at second order in dust models.

The normal frame aids in physical interpretation of nonlinear effects.

Comparison with dark energy and DGP models illustrates the framework's applicability.

Abstract

We propose a fully nonlinear framework to construct consistency relations for testing generic cosmological scenarios using the evolution of large scale structure. It is based on the covariant approach in combination with a frame that is purely given by the metric, the normal frame. As an example, we apply this framework to the LambdaCDM model, by extending the usual first order conditions on the metric potentials to second order, where the two potentials start to differ from each other. We argue that working in the normal frame is not only a practical choice but also helps with the physical interpretation of nonlinear dynamics. In this frame, effective pressures and anisotropic stresses appear at second order in perturbation theory, even for "pressureless" dust. We quantify their effect and compare them, for illustration, to the pressure of a generic clustering dark energy uid and the anisotropic stress in the DGP model. Besides, we also discuss the effect of a mismatch of the potentials on the determination of galaxy bias.