Nonlinear Relativistic Effects on Cosmological Redshift Drift

TL;DR

This paper presents the first gauge-invariant calculation of relativistic effects on cosmological redshift drift up to second order, revealing nonlinearities in the bispectrum that surpass squared power spectrum at low redshift.

Contribution

It introduces a novel gauge-invariant, second-order perturbation theory approach using light-cone coordinates to analyze relativistic effects on redshift drift.

Findings

Redshift-space distortion appears only as a second-order effect.

Derived analytical bispectrum expressions for leading-order perturbations.

Non-linearities in the bispectrum are more significant than squared power spectrum at low redshift.

Abstract

Using a fully gauge-invariant approach, we compute for the first time in the literature relativistic effects on the redshift drift up to second order in cosmological perturbation theory. This is achieved by employing a set of light-cone coordinates that simplify the description of light propagation in an inhomogeneous and anisotropic universe. We show that redshift-space distortion occurs only as a second-order effect whereas, as known, it is not present among the linear perturbations. We then derive analytical expressions of the bispectrum for the leading-order perturbative contributions on sub-Hubble scales, providing some numerical evaluations. Our finding is that, at low redshift and for large momenta, the non-linearities in the bispectrum are enhanced more than the squared power spectrum.