Abstract
Measurements of the clustering of galaxies in Fourier space, and at low wavenumbers, offer a window into the early Universe via the possible presence of scale dependent bias generated by Primordial Non Gaussianites.On such large scales a Newtonian treatment of density perturbations might not be sufficient to describe the measurements, and a fully relativistic calculation should be employed. The interpretation of the data is thus further complicated by the fact that relativistic effects break statistical homogeneity and isotropy and are potentially divergent in the Infra-Red (IR).In this work we compute for the first time the ensemble average of the most used Fourier space estimator in spectroscopic surveys, including all general relativistic (GR) effects, and allowing for an arbitrary choice of angular and radial selection functions. We show that any observable is free of IR sensitivity once all the GR terms, individually divergent, are taken into account, and that this cancellation is a consequence of the presence of the Weinberg adiabatic mode as a solution to Einstein's equations. We then study the importance of GR effects, including lensing magnification, in the interpretation of the galaxy power spectrum multipoles, finding that they are in general a small, less than ten percent level, correction to the leading redshift space distortions term. This work represents the baseline for future investigations of the interplay between Primordial Non Gaussianities and GR effects on large scales and in Fourier space.
Highlights
The cosmological interpretation of galaxy clustering data is complicated by the fact we observe the angular position and redshift of the galaxies, rather than their true physical position on the lightcone
The simple picture described above is complicated by those correlation function terms which are integrated along the line of sight (LOS), like lensing magnification and Integrated Sachs-Wolfe (ISW)
In this work we presented the first computation, in General Relativity, for the ensemble average of the Fourier space estimators traditionally used in the galaxy power spectrum analyses of spectroscopic surveys
Summary
The cosmological interpretation of galaxy clustering data is complicated by the fact we observe the angular position and redshift of the galaxies, rather than their true physical position on the lightcone. We will confirm the result in [28] for the variance of the galaxy density field, but at the same time we will show that true observed power spectrum as estimated in galaxy redshift surveys receives contributions proportional to the gravitational potential even in the absence of PNG. These terms do not show any sensitivity to long wavelength modes, which we will demonstrate is a consequence of the equivalence principle and of the existence of Weinberg adiabatic modes [6].
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