Time drift of cosmological redshifts and its variance

TL;DR

This paper derives how cosmological perturbations, especially local accelerations, affect the time drift of redshifts, estimating the magnitude of this correction relative to the primary signal.

Contribution

It provides a detailed derivation of the perturbation effects on redshift drift, highlighting the dominant role of local accelerations and quantifying their impact.

Findings

Local acceleration dominates the correction to redshift drift.

The correction amplitude is about 1% at redshift 2-4.

Using multiple absorption lines can reduce the correction to 0.1%.

Abstract

The contribution of cosmological perturbations to the time drift of the cosmological redshift is derived. It is shown that the dominant correction arises from the local acceleration of both the emitter and the observer. The amplitude of this effect is estimated to be of the order of 1% of the drift signal at z=2-4, but can easily be lowered down to 0.1% by using many absorption lines and quasars.