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Title: Single-field consistency relations of large scale structure

Abstract

We derive consistency relations for the late universe (CDM and ΛCDM): relations between an n-point 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 single-field 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 non-perturbatively in the short-scale δ. In the non-relativistic 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:
 [1];  [2];  [3];  [4]
  1. Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy)
  2. Institut de Ciències del Cosmos (ICC), Universitat de Barcelona, Martí i Franquès 1, E08028 (Spain)
  3. SISSA, via Bonomea 265, 34136, Trieste (Italy)
  4. CEA, Institut de Physique Théorique, Route Nationale, F-91191 Gif-sur-Yvette 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, E-mail: creminel@ictp.it, E-mail: jorge.norena@icc.ub.edu, E-mail: msimonov@sissa.it, E-mail: filippo.vernizzi@cea.fr. Single-field consistency relations of large scale structure. United States: N. p., 2013. Web. doi:10.1088/1475-7516/2013/12/025.
Creminelli, Paolo, Noreña, Jorge, Simonović, Marko, & Vernizzi, Filippo, E-mail: creminel@ictp.it, E-mail: jorge.norena@icc.ub.edu, E-mail: msimonov@sissa.it, E-mail: filippo.vernizzi@cea.fr. Single-field consistency relations of large scale structure. United States. doi:10.1088/1475-7516/2013/12/025.
Creminelli, Paolo, Noreña, Jorge, Simonović, Marko, and Vernizzi, Filippo, E-mail: creminel@ictp.it, E-mail: jorge.norena@icc.ub.edu, E-mail: msimonov@sissa.it, E-mail: filippo.vernizzi@cea.fr. Sun . "Single-field consistency relations of large scale structure". United States. doi:10.1088/1475-7516/2013/12/025.
@article{osti_22369862,
title = {Single-field consistency relations of large scale structure},
author = {Creminelli, Paolo and Noreña, Jorge and Simonović, Marko and Vernizzi, Filippo, E-mail: creminel@ictp.it, E-mail: jorge.norena@icc.ub.edu, E-mail: msimonov@sissa.it, E-mail: filippo.vernizzi@cea.fr},
abstractNote = {We derive consistency relations for the late universe (CDM and ΛCDM): relations between an n-point 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 single-field 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 non-perturbatively in the short-scale δ. In the non-relativistic 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 = {10.1088/1475-7516/2013/12/025},
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 single-field 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) non-perturbatively, by writing resummed consistency relations which do not require k/q⋅δ{sub q} << 1. These relations do not make any assumptions on the short-scales 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 » out in equal-time correlators. Second, we write the relations directly in redshift space, without assuming the single-stream approximation: not only the long mode affects the short scales as a homogeneous gravitational field, but it also displaces them by its velocity along the line-of-sight. Redshift space consistency relations still vanish when short modes are taken at equal time: an observation of a signal in the squeezed limit would point towards multifield inflation or a violation of the equivalence principle.« less
  • 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 3-point 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 » tiny region of the parameter space can be explored with this method. We show that no violation of the consistency relations is expected in Galileon models.« less
  • We study the symmetries of the post-recombination cosmological magnetohydrodynamical equations which describe the evolution of dark matter, baryons and magnetic fields in a self-consistent way. This is done both at the level of fluid equations and of Vlasov-Poisson-Maxwell 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 equal-time would point towards an inflationary origin of the magnetic field.
  • 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 multi-species 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 » relations with respect to the single species case. As an illustration, we discuss two physical cases in which such a velocity bias can exist: (1) a new long range scalar force in the dark matter sector (resulting in a violation of the equivalence principle in the dark matter-baryon system), and (2) the distribution of dark matter halos relative to that of the underlying dark matter field.« less
  • We generalize the single-field 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 n-point 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 n-point function. For the squeezed limit of the 3-point function, this conformal consistency relation implies that there are no terms going as 1/q{supmore » 2}. We verify that the squeezed limit of the 4-point function is related to the conformal variation of the 3-point function both in the case of canonical slow-roll inflation and in models with reduced speed of sound. In the second case the conformal consistency conditions capture, at the level of observables, the relation among operators induced by the non-linear realization of Lorentz invariance in the Lagrangian. These results mean that, in any single-field model, primordial correlation functions of ζ are endowed with an SO(4,1) symmetry, with dilations and special conformal transformations non-linearly realized by ζ. We also verify the conformal consistency relations for any n-point function in models with a modulation of the inflaton potential, where the scale dependence is not negligible. Finally, we generalize (some of) the consistency relations involving tensors and soft internal momenta.« less