Consistency relations and conservation of ζ in holographic inflation

Abstract

It is well known that, in single clock inflation, the curvature perturbation ζ is constant in time on superhorizon scales. In the standard bulk description this follows quite simply from the local conservation of the energy momentum tensor in the bulk. On the other hand, in a holographic description, the constancy of the curvature perturbation must be related to the properties of the RG flow in the boundary theory. Here, we show that, in single clock holographic inflation, the time independence of correlators of ζ follows from the cut-off independence of correlators of the energy momentum tensor in the boundary theory, and from the so-called consistency relations for vertex functions with a soft leg.

Large gauge transformation, soft theorem, and Infrared divergence in inflationary spacetime

“…It has been suggested, e.g., in refs. [3,[16][17][18][19][20], that these universal properties are both consequences of the invariance under the large gauge transformations. However, it was also revealed that this invariance is not sufficient to derive the consistency relation.…”

“…In refs. [18][19][20], the analyticity in the soft limit was additionally imposed to derive the consistency relation.…”

“…Along this line, in refs. [20,42,43], "the consistency relation" was derived starting with the dilatation invariance of the wave function in the ζ representation, Ψ[ζ] ≡ ζ|Ψ , where | ζ is the normalized eigenstate of ζ, i.e., 18) which directly follows from the invariance of the quantum state under the dilatation (2.17). 5 If and only if the WT identity which describes the insertion of ζ k=0 can be extended to the relation which describes the insertion of the soft mode ζ k with k = 0, we obtain the consistency relation: 19) where C (n) denotes the n-point function of ζ with the momentum conservation factor…”

“…In order to study the condition for the dilatation invariance of the quantum state (2.17), we decompose the wave function in terms of the eigenstates of the spatial average of ζ all over a time constant slicing, e.g., at the end of inflation, 20) JHEP10 (2017)127…”

Holography for the very early universe and the classic puzzles of hot big bang cosmology

“…The cosmological holographic framework however has already passed a number of non-trivial tests and we will provide additional support in this paper. Work on holographic cosmology was initiated in [9][10][11][12], with standard inflation fitting in this framework as a strongly coupled QFT (see for example [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]). Holographic cosmology also contains qualitative new models for the very Early Universe obtained by considering QFTs at weak coupling [33].…”