Consistency relations for the conformal mechanism

Creminelli, Paolo; Joyce, Austin; Khoury, Justin; Simonović, Marko

doi:10.1088/1475-7516/2013/04/020

Cited by 37 publications

(46 citation statements)

References 90 publications

(244 reference statements)

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“…Some other references which contain a discussion of conformal invariance and its implications for correlators in cosmology are [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Some discussion of consistency conditions which arise in the squeezed limit can be found in [14,[29][30][31][32][33][34][35][36][37][38][39][40][41]. An approach towards holography in inflationary backgrounds is given in [42,43].…”

Section: Jhep07(2014)011mentioning

confidence: 99%

Conformal invariance and the four point scalar correlator in slow-roll inflation

Ghosh

Kundu

Raju

et al. 2014

J. High Energ. Phys.

120

158

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We calculate the four point correlation function for scalar perturbations in the canonical model of slow-roll inflation. We work in the leading slow-roll approximation where the calculation can be done in de Sitter space. Our calculation uses techniques drawn from the AdS/CFT correspondence to find the wave function at late times and then calculate the four point function from it. The answer we get agrees with an earlier result in the literature, obtained using different methods. Our analysis reveals a subtlety with regard to the Ward identities for conformal invariance, which arises in de Sitter space and has no analogue in AdS space. This subtlety arises because in de Sitter space the metric at late times is a genuine degree of freedom, and hence to calculate correlation functions from the wave function of the Universe at late times, one must fix gauge completely. The resulting correlators are then invariant under a conformal transformation accompanied by a compensating coordinate transformation which restores the gauge.

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Section: Jhep07(2014)011mentioning

confidence: 99%

Conformal invariance and the four point scalar correlator in slow-roll inflation

Ghosh

Kundu

Raju

et al. 2014

J. High Energ. Phys.

120

158

View full text Add to dashboard Cite

show abstract

“…1. .1), they are actually consequences of consistency relations [52] valid in the whole class of conformal models. Furthermore, these consistency relations enable one to calculate the one-loop non-Gaussianity in the folded limit k 12 → 0.…”

Section: 1 Superhorizon Phase Perturbationsmentioning

confidence: 91%

“…Furthermore, these consistency relations enable one to calculate the one-loop non-Gaussianity in the folded limit k 12 → 0. Interestingly the one-loop contribution to the trispectrum is even more singular in the folded limit than the tree-level result (26): one finds [52] …”

Section: 1 Superhorizon Phase Perturbationsmentioning

confidence: 98%

Towards conformal cosmology

2015

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Approximate de Sitter symmetry of inflating Universe is responsible for the approximate flatness of the power spectrum of scalar perturbations. However, this is not the only option. Another symmetry which can explain nearly scale-invariant power spectrum is conformal invariance. We give a short review of models based on conformal symmetry which lead to the scale-invariant spectrum of the scalar perturbations. We discuss also potentially observable features of these models.Observational data show that primordial scalar perturbations in the Universe must have been generated at some early cosmological stage, preceding the hot epoch. They are nearly Gaussian and have nearly flat power spectrum [1]. The first property suggests that these perturbations originate from amplified vacuum fluctuations of weakly coupled quantum field(s). Indeed, the defining property of Gaussian random field ζ(x) is that it obeys the Isserlis-Wick theorem, which holds also for any free quantum field in its vacuum state, while linear evolution in classical background does not induce non-Gaussianity.The second property is also very suggestive. The power spectrum P(k) defined asgives the fluctuation in logarithmic interval of momenta,where n s is a spectral index. The flat or scale invariant spectrum corresponds to n s = 1. In early 70's Harrison, Zeldovich and Peebles and Yu [2] conjectured that the spectrum is flat, to avoid large deviation from homogeneity and isotropy of the observed Universe on large scales and black hole formation on small scales. Current observational data [1] show that the power spectrum is indded nearly flat and give n s − 1 ≈ −0.032. The flatness of the power spectrum may be due to some symmetry. The best known candidate is the symmetry SO(4, 1) of the de Sitter metric ds 2 = 1)

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“…Of course as N becomes larger, the effects become smaller and hence more difficult to observe. As such, the existence of Ward identities for conformal symmetries, that relate N to N − 1 point functions, can prove to be very relevant to our understanding of inflation [23][24][25][26][27]. The well-known consistency relation for single field inflation [28,29] between the bispectrum and the power spectrum may be an example of such a symmetry.…”

Section: Constraining the Initial State With Cosmological Datamentioning

confidence: 99%

What Is the Shape of the Initial State?

Agarwal

Holman

Tolley

2013

Int. J. Mod. Phys. D

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We argue that a plausible operational definition for an initial state of the Universe is the initial quantum state of the curvature perturbations generated during inflation. We provide a parameterization of this state and generalize the standard in-in formalism to incorporate the structures in this state into the computation of correlators of the perturbations. Measurements of these correlators using both the CMB as well as large scale structure probe different structures in the initial state, as they give rise to bi-and tri-spectra peaked on different shapes of triangles and quadrilaterals in momentum space. In essence, the shapes implied by the correlators feed directly into information about the shape of the initial state and what physics could have preceded inflation to set this state up.1 Essay awarded second prize in the Gravity Research Foundation 2013 essay competition arXiv:1305.3615v2 [hep-th] Dec 2013How can we access information about the initial state of the Universe? First of all it would be useful to have a definition of this state which, all parties can agree, represents something that makes sense as an initial state. Part and parcel of arriving at such a definition would be the requirement that this state can be probed experimentally.Our main signpost in the search for an initial state is inflation [1][2][3], which has become the dominant paradigm to explain the large-scale homogeneity of the Universe and generate the initial perturbations that seeded cosmic structure. It is also becoming increasingly possible to probe the physics of inflation using excellent cosmological observations from the cosmic microwave background (CMB) and large scale structure (LSS).In an ideal world, we would have access to a full theory of quantum gravity at both weak and strong coupling and be able to input test initial quantum states for the relevant variables in such a theory, calculate observables emerging from these initial conditions, and then compare those results to observations. Unfortunately, we are far from living in such a world and must rely on proxies, such as quantum field theory defined in a curved spacetime. This technology [4,5] has been used to predict the evaporation of black holes, as well as to calculate the quantum fluctuations of fields in an inflationary cosmology [6][7][8][9][10][11]; it is this latter application that will be of interest to us below.This leads us to our definition of the initial state of the Universe: it is the quantum state of the curvature perturbations generated during inflation. Now, it is easy to argue that there is surely a pre-inflationary era and any initial state must refer to this era. But inflation is the great eraser; given a sufficient number of e-folds, pre-inflationary effects can be suppressed to unobservable levels. Thus, from an operational point of view, if inflation happened at all, an event that seems more and more likely with the release of every new cosmological data set, our ability to infer the state of the early universe will be limited ...

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Consistency relations for the conformal mechanism

Cited by 37 publications

References 90 publications

Conformal invariance and the four point scalar correlator in slow-roll inflation

Conformal invariance and the four point scalar correlator in slow-roll inflation

Towards conformal cosmology

What Is the Shape of the Initial State?

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