Inflation in Flatland

Hinterbichler, Kurt; Joyce, Austin; Khoury, Justin

doi:10.1088/1475-7516/2017/01/044

Cited by 6 publications

(11 citation statements)

References 77 publications

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“…As we mentioned at the outset, the subject of asymptotic symmetries has a wide range of applications, and our results give a new perspective on these applications. For example, in cosmology, the change in the curvature perturbation, ζ, produced by an asymptotic symmetry transformation of dS 3 is identified with adiabatic modes of ζ [40]. The relation to the membrane paradigm described in the present paper allows one to interpret the perturbations produced by adiabatic modes as changes in the energy density of the boundary fluid as observed by a null observer (c.f.…”

Section: Discussionmentioning

confidence: 75%

Asymptotic symmetries of three dimensional gravity and the membrane paradigm

González

Penna

2019

J. High Energ. Phys.

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The asymptotic symmetry group of three-dimensional (anti) de Sitter space is the two dimensional conformal group with central charge c = 3 /2G. Usually the asymptotic charge algebra is derived using the symplectic structure of the bulk Einstein equations. Here, we derive the asymptotic charge algebra by a different route. First, we formulate the dynamics of the boundary as a 1+1-dimensional dynamical system. Then we realize the boundary equations of motion as a Hamiltonian system on the dual Lie algebra, g * , of the two-dimensional conformal group. Finally, we use the Lie-Poisson bracket on g * to compute the asymptotic charge algebra. This streamlines the derivation of the asymptotic charge algebra because the Lie-Poisson bracket on the boundary is significantly simpler than the symplectic structure derived from the bulk Einstein equations. It also clarifies the analogy between the infinite dimensional symmetries of gravity and fluid dynamics.1 Here "small diffeomorphisms" means diffeomorphisms which act trivially at asymptotic infinity. 2 Of course, in this example the redundancy is not a gauge redundancy.

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Section: Discussionmentioning

confidence: 75%

Asymptotic symmetries of three dimensional gravity and the membrane paradigm

González

Penna

2019

J. High Energ. Phys.

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“…There exist both scalar consistency relations relating the squeezed limit of the

(n + 1)

‐point correlators to the n ‐point correlators of scalar perturbations and tensor consistency relations involving tensor and scalar modes (see also ). Recently, it has been shown that the consistency relations are in close connection with the asymptotic symmetries of de Sitter space since soft degrees of freedom produced by the expansion of de Sitter can be interpreted as the Nambu‐Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime.…”

Section: Consistency Relations From the Ds/cft3 Correspondence Radiamentioning

confidence: 99%

“…Bulk fields

ϕ (\vec{x}, η)

evolving in four‐dimensional de Sitter spacetime and behaving near the boundary

η = 0

(η being the conformal time) as

ϕ false(\overset{x}{true}, η false) \sim {(- η)}^{normalΔ} ϕ false(\overset{x}{true} false)

correspond on the three‐dimensional space, where the symmetry is CFT 3 , to a field of conformal weight

h = Δ - 3

. Correlators of fields excited during a de Sitter phase are therefore expected to be constrained by conformal invariance and the literature on this topic is rich and diverse . In particular, much attention has been devoted to the relation among the consistency relations, soft theorems and the asymptotic symmetries of de Sitter which transform asymptotic vacua to new physically inequivalent vacua by generating long perturbation modes .…”

Section: Introductionmentioning

confidence: 99%

“…Correlators of fields excited during a de Sitter phase are therefore expected to be constrained by conformal invariance and the literature on this topic is rich and diverse . In particular, much attention has been devoted to the relation among the consistency relations, soft theorems and the asymptotic symmetries of de Sitter which transform asymptotic vacua to new physically inequivalent vacua by generating long perturbation modes .…”

Section: Introductionmentioning

confidence: 99%

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Inflation and conformal invariance: the perspective from radial quantization

Kehagias

Riotto

2017

Fortschritte der Physik

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According to the dS/CFT correspondence, correlators of fields generated during a primordial de Sitter phase are constrained by three-dimensional conformal invariance. Using the properties of radially quantized conformal field theories and the operator-state correspondence, we glean information on some points. The Higuchi bound on the masses of spin-s states in de Sitter is a direct consequence of reflection positivity in radially quantized CFT 3 and the fact that scaling dimensions of operators are energies of states. The partial massless states appearing in de Sitter correspond from the boundary CFT 3 perspective to boundary states with highest weight for the conformal group. We discuss inflationary consistency relations and the role of asymptotic symmetries which transform asymptotic vacua to new physically inequivalent vacua by generating long perturbation modes. We show that on the CFT 3 side, asymptotic symmetries have a nice quantum mechanics interpretation. For instance, acting with the asymptotic dilation symmetry corresponds to evolving states forward (or backward) in "time" and the charge generating the asymptotic symmetry transformation is the Hamiltonian itself. Finally, we investigate the symmetries of anisotropic inflation and show that correlators of four-dimensional free scalar fields can be reproduced in the dual picture by considering an isotropic three-dimensional boundary enjoying dilation symmetry, but with a nonvanishing vacuum expectation value of the boundary stress-energy momentum tensor.

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“…A deep connection between these soft theorems and asymptotic symmetries of asymptotically-flat spaces has been suggested [19][20][21][22][23][24][25][26]. In a similar way, cosmological soft theorems are related to the asymptotic symmetries of cosmological spacetimes [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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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Inflation in Flatland

Cited by 6 publications

References 77 publications

Asymptotic symmetries of three dimensional gravity and the membrane paradigm

Asymptotic symmetries of three dimensional gravity and the membrane paradigm

Inflation and conformal invariance: the perspective from radial quantization

Inflationary soft theorems revisited: a generalized consistency relation

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