The observed galaxy power spectrum in General Relativity

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.

44 pages, 11 figures

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Cited by in corpus (15)

• Constraints on Multi-Field Inflation from the BOSS Galaxy Survey
• Can we actually constrain $f_{\mathrm{NL}}$ using the scale-dependent bias effect? An illustration of the impact of galaxy bias uncertainties using the BOSS DR12 galaxy power spectrum
• Cosmological inference from the EFTofLSS: the eBOSS QSO full-shape analysis
• Bispectrum-window convolution via Hankel transform
• Wide-angle and relativistic effects in Fourier-space clustering statistics
• Constraining primordial non-Gaussianity by combining next-generation galaxy and 21 cm intensity mapping surveys
• Wide-angle effects in multi-tracer power spectra with Doppler corrections
• Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole
• The galaxy power spectrum on the lightcone: deep, wide-angle redshift surveys and the turnover scale
• Contributions from primordial non-Gaussianity and General Relativity to the galaxy power spectrum
• Large gauge transformations, local coordinates and cosmological observables
• Incompatibility of Standard Galaxy Bias Models in General Relativity
• Relativistic matter bispectrum of cosmic structures on the light cone
• The Kaiser-Rocket effect: three decades and counting
• Quijote PNG: The information content of the halo power spectrum and bispectrum