TY - JOUR

T1 - Consequences of symmetries and consistency relations in the large-scale structure of the universe for non-local bias and modified gravity

AU - Kehagias, A.

AU - Noreña, J.

AU - Perrier, H.

AU - Riotto, A.

N1 - Funding Information:
When completing this work, Ref. [51] appeared. Our results, when overlap is possible, agree with theirs. We thank M. Pietroni and M. Peloso for useful correspondence. We acknowledge related work by P. Creminelli, J. Gleyzes, M. Simonović and F. Vernizzi and thank them for spotting an omission in the consistency relation in redshift space in an earlier version of this draft. H.P., J.N. and A.R. are supported by the Swiss National Science Foundation (SNSF), project “The non-Gaussian Universe” (project number: 200021140236 ). The research of A.K. was implemented under the “Aristeia” Action of the “Operational Programme Education and Lifelong Learning” and is co-funded by the European Social Fund (ESF) and National Resources. It is partially supported by European Union's Seventh Framework Programme (FP7/2007–2013) under REA grant agreement No. 329083 .

PY - 2014/6

Y1 - 2014/6

N2 - Consistency relations involving the soft limit of the (n + 1)-correlation 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 constrains 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 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 breakdown of the so-called non-local Eulerian bias model or the violation of the equivalence principle in the underlying theory of gravity.

AB - Consistency relations involving the soft limit of the (n + 1)-correlation 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 constrains 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 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 breakdown of the so-called non-local Eulerian bias model or the violation of the equivalence principle in the underlying theory of gravity.

UR - http://www.scopus.com/inward/record.url?scp=84897481001&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2014.03.020

DO - 10.1016/j.nuclphysb.2014.03.020

M3 - Article

AN - SCOPUS:84897481001

SN - 0550-3213

VL - 883

SP - 83

EP - 106

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 1

ER -