Galaxy Bias and non-Linear Structure Formation in General Relativity

By T. Baldauf, Uros Seljak, L. Senatore, M. Zaldarriaga. 2011

179 citations recorded by the source corpus.

Length scales probed by the large scale structure surveys are becoming closer and closer to the horizon scale. Further, it has been recently understood that non-Gaussianity in the initial conditions could show up in a scale dependence of the bias of galaxies at the largest possible distances. It is therefore important to take General Relativistic effects into account. Here we provide a General Relativistic generalization of the bias that is valid both for Gaussian and for non-Gaussian initial conditions. The collapse of objects happens on very small scales, while long-wavelength modes are always in the quasi linear regime. Around every small collapsing region, it is therefore possible to find a reference frame that is valid for arbitrary times and where the space time is almost flat: the Fermi frame. Here the Newtonian approximation is applicable and the equations of motion are the ones of the standard N-body codes. The effects of long-wavelength modes are encoded in the mapping from the cosmological frame to the local Fermi frame. At the level of the linear bias, the effect of the long-wavelength modes on the dynamics of the short scales is all encoded in the local curvature of the Universe, which allows us to define a General Relativistic generalization of the bias in the standard Newtonian setting. We show that the bias due to this effect goes to zero as the square of the ratio between the physical wavenumber and the Hubble scale for modes longer than the horizon, confirming the intuitive picture that modes longer than the horizon do not have any dynamical effect. On the other hand, the bias due to non-Gaussianities does not need to vanish for modes longer than the Hubble scale, and for non-Gaussianities of the local kind it goes to a constant. As a further application of our setup, we show that it is not necessary to perform large N-body simulations to extract information about long-wavelength modes: N-body simulations can be done on small scales and long-wavelength modes are encoded simply by adding curvature to the simulation, as well as rescaling the time and the scale.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/d03633484c2a82474821b6453e32384925ea985c

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Citations in the corpus

Testing Inflation with Large Scale Structure: Connecting Hopes with Reality (2014, background): “Long modes can be thought of as producing a curved universe with a curvature parameter ΩK ∼ q2ζ/a2H2 on which the short modes evolve [22, 23].”
Biased Tracers in Redshift Space in the EFT of Large-Scale Structure (2016, methodology): “Methods to measure the parameters of the EFTofLSS from small numerical simulations have been developed in [3, 34, 35, 36, 31].”
The CLASSgal code for relativistic cosmological large scale structure (2013, methodology): “In the numerical calculations of the present paper we assume for simplicity b = 1, for a detailed discussion of galaxy bias in General Relativity see [24].”
The cosmological analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure (2019, unknown): “For example, one could consider if it is possible to extend techniques such as the ‘separate universe approach’ (see for example [93, 94, 95, 96, 97]) to include galaxies in a reliable way.”
The effective field theory of cosmological large scale structures (2012, background): “This has been indeed recently elucidated in the context of the bias, where it was shown that in order to derive the bias on large scales one needs to run very small simulations in a curved universe [3].”