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 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, fNLloc, 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 fNLloc by (10–30)%, if external information on the bias parameters is available.
Highlights
Fluctuations with wavelengths larger than the volume of a galaxy survey affect the measurement of the galaxy power spectrum within the survey itself
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
In this paper we investigated the effect of super-survey modes on the galaxy power spectrum in the presence of primordial non-Gaussianity
Summary
In a survey of volume Vs and typical size Ls Vs1/3, the main observable is the product of the underlying galaxy density field, δg(x), with the survey window function, W (x), δg(x, z) = δg(x, z)W (x). Where δ(p, z) and W (−p) are the Fourier Transform of the density field and window function respectively. In this work we assume the window function is spherically symmetric and normalized to unity, e.g. a spherical top-hat, such that the variance of the long mode reads σL2. The mean value of the DM density and tidal fields in the survey volume, ∆L, is a number drawn from a Gaussian with mean zero and variance σL2. A more rigorous treatment of super sample modes should include relativistic contributions to galaxy clustering and their possible correlation with the long wavelength fields. In this work we assume a Planck+BAO fiducial cosmology [67]
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