Local Primordial Non-Gaussianities and Super-Sample Variance

TL;DR

This paper investigates how large-scale gravitational potential fluctuations influence measurements of primordial non-Gaussianities in galaxy surveys, revealing that super-sample modes can slightly improve constraints on $f_{NL}^{loc}$ under certain conditions.

Contribution

It introduces the first computation of the response of the redshift-space galaxy power spectrum to a long-wavelength gravitational potential, including stochastic effects and bias couplings.

Findings

Super-sample modes have minimal impact on $f_{NL}^{loc}$ constraints.

External bias information can improve $f_{NL}^{loc}$ measurement accuracy.

Super-sample effects may reduce error bars on primordial non-Gaussianity estimates.

Abstract

Fluctuations with wavelengths larger than the volume of a galaxy survey affect the measurement of the galaxy power spectrum within the survey itself. In the presence of local Primordial Non- Gaussianities (PNG), in addition to the super-sample matter density and tidal fluctuations, the large-scale gravitational potential also induces a modulation of the observed power spectrum. In this work we investigate this modulation by computing for the first time the response of the redshift-space galaxy power spectrum to the presence of a long wavelength gravitational potential, fully accounting for the stochastic contributions. For biased tracers new response functions arise due to couplings between the small-scale fluctuations in the density, velocity and gravitational fields, the latter through scale dependent bias operators, and the large-scale gravitational potential. We study the impact of the super-sample modes on the measurement of the amplitude of the primordial bispectrum of the local-shape, $f_{\rm NL}^{\rm loc}$, accounting for modulations of both the signal and the covariance of the galaxy power spectrum by the long modes. Considering DESI-like survey specifications, we show that in most cases super-sample modes cause little or no degradation of the constraints, and could actually reduce the errorbars on $f_{\rm NL}^{\rm loc}$ by (10 - 30)\%, if external information on the bias parameters is available.