General relativistic effects in the galaxy bias at second order

Abstract

The local galaxy bias formalism relies on the energy constraint equation at the formation time to relate the metric perturbation to the matter density contrast. In the Newtonian approximation, this relationship is linear, which allows us to specify the initial galaxy density as a function of local physical operators. In general relativity however, the relationship is intrinsically nonlinear and a modulation of the short-wavelength mode by the long-wavelength mode might be expected. We describe in detail how to obtain local coordinates where the coupling of the long- to the short-wavelength modes is removed through a change of coordinates (in the absence of the primordial non-Gaussianity). We derive the general-relativistic correction to the galaxy bias expansion at second order. The correction does not come from the modulation of small-scale clustering by the long-wavelength mode; instead, it arises from distortions of the volume element by the long-wavelength mode and it does not lead to new bias parameters.

Version accepted by JCAP. Key contributions clearly summarised. Few typos fixed

References in corpus (8)

• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• Conformal Symmetries of Adiabatic Modes in Cosmology
• How Gaussian can our Universe be?
• General relativistic weak-field limit and Newtonian N-body simulations
• Einstein's signature in cosmological large-scale structure
• Relativistic Lagrangian displacement field and tensor perturbations
• Large-Scale Tides in General Relativity

Cited by in corpus (2)

• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Local primordial non-Gaussianity in the relativistic galaxy bispectrum