Galaxy power spectrum in general relativity

Abstract

We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to k−4Pm(k) or k−2Pm(k) on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment cannot be measured. We find that the unphysical infrared divergence obtained in previous calculations occurred only due to not considering all general relativistic contributions consistently. Despite the absence of divergent terms, general relativistic effects represented by non-divergent terms alter the galaxy power spectrum at large scales (smaller than the horizon scale). In our numerical computation of the full galaxy power spectrum, we show the deviations from the standard redshift-space power spectrum due to these non-divergent corrections. We conclude that, as relativistic effects significantly alter the galaxy power spectrum at k≲ keq, they need to be taken into account in the analysis of large-scale data.

Monopole fluctuation of the CMB and its gauge invariance

“…For our calculations, a uniform gravitational potential corresponds to the constant contributions in individual transfer functions such as T ψ , while a uniform gravitational acceleration corresponds to the contributions in proportion to k (or the gradient of the potential contributions). It was shown [34][35][36][37] that the theoretical descriptions of the luminosity distance and galaxy clustering are devoid of such contributions.…”

Contributions from primordial non-Gaussianity and General Relativity to the galaxy power spectrum

“…As mentioned earlier, a few recent works have argued that a divergent behaviour on large scales of the galaxy power spectrum due to the relativistic corrections is nonphysical [35,38,39]. In order to avoid such divergence, a coordinate transformation must be performed, which places the observed spectrum in a "local frame" where the divergences disappear.…”

“…More recently, methods to avoid the infrared divergences of relativistic contributions in the galaxy power spectrum, have been proposed in Refs. [38,39].…”

Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole

“…Most of the early computations of projection effects did not account for all the observer terms, which are essential for the interpretation of the monopole (see e.g. [25][26][27] for different views on this question). Below, we will take into account the observer terms properly and clarify their relation to the cosmic-ruler observables, and to the choice of background.…”