Singlefield consistency relations of large scale structure
Abstract
We derive consistency relations for the late universe (CDM and ΛCDM): relations between an npoint function of the density contrast δ and an (n+1)point function in the limit in which one of the (n+1) momenta becomes much smaller than the others. These are based on the observation that a long mode, in singlefield models of inflation, reduces to a diffeomorphism since its freezing during inflation all the way until the late universe, even when the long mode is inside the horizon (but out of the sound horizon). These results are derived in Newtonian gauge, at first and second order in the small momentum q of the long mode and they are valid nonperturbatively in the shortscale δ. In the nonrelativistic limit our results match with [1]. These relations are a consequence of diffeomorphism invariance; they are not satisfied in the presence of extra degrees of freedom during inflation or violation of the Equivalence Principle (extra forces) in the late universe.
 Authors:
 Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy)
 Institut de Ciències del Cosmos (ICC), Universitat de Barcelona, Martí i Franquès 1, E08028 (Spain)
 SISSA, via Bonomea 265, 34136, Trieste (Italy)
 CEA, Institut de Physique Théorique, Route Nationale, F91191 GifsurYvette cédex (France)
 Publication Date:
 OSTI Identifier:
 22369862
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2013; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DEGREES OF FREEDOM; DENSITY; EQUIVALENCE PRINCIPLE; FREEZING; FUNCTIONS; RELATIVISTIC RANGE; UNIVERSE; COSMOLOGICAL INFLATION
Citation Formats
Creminelli, Paolo, Noreña, Jorge, Simonović, Marko, and Vernizzi, Filippo, Email: creminel@ictp.it, Email: jorge.norena@icc.ub.edu, Email: msimonov@sissa.it, Email: filippo.vernizzi@cea.fr. Singlefield consistency relations of large scale structure. United States: N. p., 2013.
Web. doi:10.1088/14757516/2013/12/025.
Creminelli, Paolo, Noreña, Jorge, Simonović, Marko, & Vernizzi, Filippo, Email: creminel@ictp.it, Email: jorge.norena@icc.ub.edu, Email: msimonov@sissa.it, Email: filippo.vernizzi@cea.fr. Singlefield consistency relations of large scale structure. United States. doi:10.1088/14757516/2013/12/025.
Creminelli, Paolo, Noreña, Jorge, Simonović, Marko, and Vernizzi, Filippo, Email: creminel@ictp.it, Email: jorge.norena@icc.ub.edu, Email: msimonov@sissa.it, Email: filippo.vernizzi@cea.fr. Sun .
"Singlefield consistency relations of large scale structure". United States.
doi:10.1088/14757516/2013/12/025.
@article{osti_22369862,
title = {Singlefield consistency relations of large scale structure},
author = {Creminelli, Paolo and Noreña, Jorge and Simonović, Marko and Vernizzi, Filippo, Email: creminel@ictp.it, Email: jorge.norena@icc.ub.edu, Email: msimonov@sissa.it, Email: filippo.vernizzi@cea.fr},
abstractNote = {We derive consistency relations for the late universe (CDM and ΛCDM): relations between an npoint function of the density contrast δ and an (n+1)point function in the limit in which one of the (n+1) momenta becomes much smaller than the others. These are based on the observation that a long mode, in singlefield models of inflation, reduces to a diffeomorphism since its freezing during inflation all the way until the late universe, even when the long mode is inside the horizon (but out of the sound horizon). These results are derived in Newtonian gauge, at first and second order in the small momentum q of the long mode and they are valid nonperturbatively in the shortscale δ. In the nonrelativistic limit our results match with [1]. These relations are a consequence of diffeomorphism invariance; they are not satisfied in the presence of extra degrees of freedom during inflation or violation of the Equivalence Principle (extra forces) in the late universe.},
doi = {10.1088/14757516/2013/12/025},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 12,
volume = 2013,
place = {United States},
year = {Sun Dec 01 00:00:00 EST 2013},
month = {Sun Dec 01 00:00:00 EST 2013}
}

We generalize the recently derived singlefield consistency relations of Large Scale Structure in two directions. First, we treat the effect of the long modes (with momentum q) on the short ones (with momentum k) nonperturbatively, by writing resummed consistency relations which do not require k/q⋅δ{sub q} << 1. These relations do not make any assumptions on the shortscales physics and are extended to include (an arbitrary number of) multiple long modes, internal lines with soft momenta and soft loops. We do several checks of these relations in perturbation theory and we verify that the effect of soft modes always cancelsmore »

Singlefield consistency relations of large scale structure part III: test of the equivalence principle
The recently derived consistency relations for Large Scale Structure do not hold if the Equivalence Principle (EP) is violated. We show it explicitly in a toy model with two fluids, one of which is coupled to a fifth force. We explore the constraints that galaxy surveys can set on EP violation looking at the squeezed limit of the 3point function involving two populations of objects. We find that one can explore EP violations of order 10{sup −3}÷10{sup −4} on cosmological scales. Chameleon models are already very constrained by the requirement of screening within the Solar System and only a verymore » 
Testing the origin of cosmological magnetic fields through the largescale structure consistency relations
We study the symmetries of the postrecombination cosmological magnetohydrodynamical equations which describe the evolution of dark matter, baryons and magnetic fields in a selfconsistent way. This is done both at the level of fluid equations and of VlasovPoissonMaxwell equations in phase space. We discuss some consistency relations for the soft limit of the (n+1)correlator functions involving magnetic fields and matter overdensities. In particular, we stress that any violation of such consistency relations at equaltime would point towards an inflationary origin of the magnetic field. 
Ward identities and consistency relations for the large scale structure with multiple species
We present fully nonlinear consistency relations for the squeezed bispectrum of Large Scale Structure. These relations hold when the matter component of the Universe is composed of one or more species, and generalize those obtained in [1,2] in the single species case. The multispecies relations apply to the standard dark matter + baryons scenario, as well as to the case in which some of the fields are auxiliary quantities describing a particular population, such as dark matter halos or a specific galaxy class. If a large scale velocity bias exists between the different populations new terms appear in the consistencymore » 
Conformal consistency relations for singlefield inflation
We generalize the singlefield consistency relations to capture not only the leading term in the squeezed limit — going as 1/q{sup 3}, where q is the small wavevector — but also the subleading one, going as 1/q{sup 2}. This term, for an (n+1)point function, is fixed in terms of the variation of the npoint function under a special conformal transformation; this parallels the fact that the 1/q{sup 3} term is related with the scale dependence of the npoint function. For the squeezed limit of the 3point function, this conformal consistency relation implies that there are no terms going as 1/q{supmore »