Large-Scale Structure Observables in General Relativity

TL;DR

This paper reviews how to define and compute key large-scale structure observables in the universe within a general relativistic framework, providing covariant, gauge-invariant formulas for linear perturbations.

Contribution

It offers a comprehensive, covariant, gauge-invariant formulation of large-scale structure observables in linear perturbation theory within general relativity.

Findings

Derived covariant, gauge-invariant expressions for redshift perturbation, cosmic ruler distortion, and number density.

Includes scalar, vector, and tensor metric perturbations in a flat FRW universe.

Framework can be extended to higher-order perturbations.

Abstract

We review recent studies that rigorously define several key observables of the large-scale structure of the Universe in a general relativistic context. Specifically, we consider i) redshift perturbation of cosmic clock events; ii) distortion of cosmic rulers, including weak lensing shear and magnification; iii) observed number density of tracers of the large-scale structure. We provide covariant and gauge-invariant expressions of these observables. Our expressions are given for a linearly perturbed flat Friedmann-Robertson-Walker metric including scalar, vector, and tensor metric perturbations. While we restrict ourselves to linear order in perturbation theory, the approach can be straightforwardly generalized to higher order.