Soft theorems for shift-symmetric cosmologies

Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca

doi:10.1103/physrevd.97.063531

Cited by 58 publications

(106 citation statements)

References 20 publications

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“…Ultra-slow-roll inflation, while strictly a single field model, has essentially an extra clock due to the importance of what normally would be discarded as the decaying mode. See[10,[28][29][30].…”

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confidence: 99%

Nonperturbative test of consistency relations and their violation

Esposito

Hui

2019

Phys. Rev. D

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In this paper, we verify the large scale structure consistency relations using N -body simulations, including modes in the highly non-linear regime. These relations (pointed out by Kehagias & Riotto and Peloso & Pietroni) follow from the symmetry of the dynamics under a shift of the Newtonian potential by a constant and a linear gradient, and predict the absence of certain poles in the ratio between the (equal time) squeezed bispectrum and power spectrum. The consistency relations, as symmetry statements, are exact, but have not been previously checked beyond the perturbative regime. Our test using N -body simulations not only offers a non-perturbative check, but also serves as a warm-up exercise for applications to observational data. A number of subtleties arise when taking the squeezed limit of the bispectrum-we show how to circumvent or address them. An interesting by-product of our investigation is an explicit demonstration that the linear-gradientsymmetry is unaffected by the periodic boundary condition of the simulations. Lastly, we verify using simulations that the consistency relations are violated when the initial conditions are nongaussian (of the local f NL type). The methodology developed here paves the way for constraining primordial non-gaussianity using large scale structure data, including (numerous) highly non-linear modes that are otherwise hard to interpret and utilize.1 The split into two separate symmetries here follows the discussion of [17].

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confidence: 99%

Nonperturbative test of consistency relations and their violation

Esposito

Hui

2019

Phys. Rev. D

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“…In the case of ultra-slow roll, it is precisely the violation of the physical mode condition that invalidates the late-time (equal-time) statement (6.2) corresponding to the dilation or SCT symmetry. However, as noted by [62,63], in these models there can be a second adiabatic mode, which does satisfy the physical mode condition (see discussion in Section 5), thus giving rise to a modified late-time consistency relation. This interesting relation pointed out by [62,63] requires additional transformations beyond spatial dilation and SCT.…”

Section: Discussionmentioning

confidence: 98%

Inflationary soft theorems revisited: a generalized consistency relation

Hui

Joyce

Wong

2019

J. Cosmol. Astropart. Phys.

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We reconsider the derivation of soft theorems associated with nonlinearly-realized symmetries in cosmology. Utilizing the path integral, we derive a generalized consistency relation that relates a squeezed (N + 1)-point correlation function to an N -point function, where the relevant soft mode is at early rather than late time. This generalized (early-late-time) version has wider applicability than the standard consistency relation where all modes are evaluated at late times. We elucidate the conditions under which the latter follows from the former. A key ingredient is the physical mode condition: that the nonlinear part of the symmetry transformation must match the time dependence of the dominant, long wavelength physical mode. This is closely related to, but distinct from, the adiabatic mode condition. Our derivation sheds light on a number of otherwise puzzling features of the standard consistency relation: (1) the underlying nonlinearly-realized symmetries (such as dilation and special conformal transformation SCT) originate as residual gauge redundancies, yet the consistency relation has physical content-for instance, it can be violated; (2) the standard consistency relation is known to fail in ultraslow-roll inflation, but since dilation and SCT remain good symmetries, there should be a replacement for the standard relation; (3) in large scale structure applications, it is known that the standard consistency relation breaks down if the long wavelength power spectrum is too blue. The early-late-time consistency relation helps address these puzzles. We introduce a toy model where explicit checks of this generalized consistency relation are simple to carry out. Our methodology can be adapted to cases where violations of the standard consistency relation involve additional light degrees of freedom beyond the inflaton. * 8 We often switch between the singular and plural form for "consistency relation". The singular form refers to the one that holds for all relevant symmetries (such as (2.22)), whereas the plural form counts one for each symmetry separately (such as dilation consistency relation, SCT consistency relation and so on). 9 We follow convention and sometimes refer to the consistency relation as an "identity", but it should be emphasized the consistency relation has non-trivial physical content, as explained above and further in Section 2.2.

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“…Hence, we only have to sum over 8, rather than 24, permutations of the momenta. We also perform a summation over three 22 directions of q u that are mutually orthogonal, but otherwise arbitrary. There are three types of scalar-exchange diagrams that differ by the type of vertices, shown on Fig.…”

Section: A Perturbations Around Flrwmentioning

confidence: 99%

Spatial curvature at the sound horizon

Avis¹,

Jazayeri²,

Pajer³

et al. 2020

J. Cosmol. Astropart. Phys.

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The effect of spatial curvature on primordial perturbations is controlled by Ω K,0 /c 2 s , where Ω K,0 is today's fractional density of spatial curvature and c s is the speed of sound during inflation. Here we study these effects in the limit c s 1. First, we show that the standard cosmological soft theorems in flat universes are violated in curved universes and the soft limits of correlators can have non-universal contributions even in single-clock inflation. This is a consequence of the fact that, in the presence of spatial curvature, there is a gap between the spectrum of residual diffeomorphisms and that of physical modes. Second, there are curvature corrections to primordial correlators, which are not scale invariant. We provide explicit formulae for these corrections to the power spectrum and the bispectrum to linear order in curvature in single-clock inflation. We show that the large-scale CMB anisotropies could provide interesting new constraints on these curvature effects, and therefore on Ω K,0 /c 2 s , but it is necessary to go beyond our linear-order treatment.

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Soft theorems for shift-symmetric cosmologies

Cited by 58 publications

References 20 publications

Nonperturbative test of consistency relations and their violation

Nonperturbative test of consistency relations and their violation

Inflationary soft theorems revisited: a generalized consistency relation

Spatial curvature at the sound horizon

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