Long gradient mode and large-scale structure observables I: linear order

TL;DR

This paper demonstrates that long gradient modes, which are gauge artifacts, do not influence large-scale cosmological observables at linear order, confirming the gauge invariance of these measurements.

Contribution

It confirms that genuine relativistic large-scale observables are unaffected by long gradient modes at linear order, validating current gauge-invariant methods.

Findings

Long gradient modes leave no imprint on large-scale observables at first order.

Relativistic bias relations for halos and galaxies are invariant under long gradient mode perturbations.

The observed power spectrum remains unaffected by long gradient modes.

Abstract

We study the effect of long gradient modes on large scale observables. When defined correctly, genuine observables should not only be gauge invariant but also devoid of any gauge artifacts. One such gauge artifact is a pure gradient mode. Using the relativistic formulation of large scale observables, we confirm that a long gradient mode which is still outside observer's horizon leaves no imprint on the large scale observables at first order. These include the cosmic rulers and the number counts. This confirms the existing method for relativistically defined observables. The general relativistic bias relation for the halos and galaxies is also invariant under the presence of a long gradient mode perturbation. The observed power spectrum is not affected by this long mode.