Consequences of Symmetries and Consistency Relations in the Large-Scale Structure of the Universe for Non-local bias and Modified Gravity

TL;DR

This work shows that the symmetries of Newtonian dark-matter and galaxy fluids enforce consistency relations for large-scale structure in both real and redshift space. These relations imply that galaxy bias must be non-local and can be expressed in terms of invariants like $ abla^2oldsymbol{v}$ and $s_{ij}$, with Lifshitz scaling determining the time evolution of bias coefficients. The authors verify the tree-level and one-loop bispectrum consistency relations within the non-local bias framework and extend the relations to redshift space, highlighting how observations in galaxy surveys can test these symmetries. Moreover, they demonstrate that equivalence-principle-violating modified gravity can lead to violations of the consistency relations, offering a potential observational signature of new infrared physics; thus, deviations from the predicted squeezed-limit behavior would indicate either breakdown of the non-local Eulerian bias model or EP violation in gravity.

Abstract

Consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter and galaxy overdensities can be obtained, both in real and redshift space, thanks to the symmetries enjoyed by the Newtonian equations of motion describing the dark matter and galaxy fluids coupled through gravity. We study the implications of such symmetries for the theory of galaxy bias and for the theories of modified gravity. We find that the invariance of the fluid equations under a coordinate transformation that induces a long-wavelength velocity constrain the bias to depend only on a set of invariants, while the symmetry of such equations under Lifshitz scalings in the case of matter domination allows one to compute the time-dependence of the coefficients in the bias expansion. We also find that in theories of modified gravity which violate the equivalence principle induce a violation of the consistency relation which may be a signature for their observation. Thus, given adiabatic Gaussian initial conditions, the observation of a deviation from the consistency relation for galaxies would signal a break-down of the so-called non-local Eulerian bias model or the violation of the equivalence principle in the underlying theory of gravity.

Figures (1)

• Figure 1: Schematic representation of a large-scale spherical over-density of radius $R_0$ where the chameleon field is screened, and in the presence of a long-wavelength perturbation of the gravitational field (here represented by the dark blue dashed line). The consistency relation will be given by the correlation of the modulation of the power spectrum with the long-wavelength gravitational field. The case (a) corresponds to the case in which the galaxies are all in the screened region, Eq. (\ref{['deltadelta22']}), case (c) corresponds to the case in which all the galaxies are in the unscreened region, Eq. (\ref{['delta-eq2']}), and case (b) corresponds to the case in which there are both screened and unscreened galaxies, Eq. (\ref{['delta-eq1']}).