Comparison of dynamical and spectator models of a (pseudo)conformal universe

Abstract

We discuss two versions of the conformal scenario for generating scalar cosmological perturbations: a spectator version with a scalar field conformally coupled to gravity and carrying negligible energy density, and a dynamical version with a scalar field minimally coupled to gravity and dominating the cosmological evolution. By making use of the Newtonian gauge, we show that (i) no UV strong coupling scale is generated below M P l due to mixing with metric perturbations in the dynamical scenario, and (ii) the dynamical and spectator models yield identical results to the leading nonlinear order. We argue that these results, which include potentially observable effects like statistical anisotropy and non-Gaussianity, are characteristic of the entire class of conformal models. As an example, we reproduce, within the dynamical scenario and working in comoving gauge, our earlier result on the statistical anisotropy, which was originally obtained within the spectator approach.

Consistency relations for the conformal mechanism

“…In this paper we only studied correlation functions in the absence of gravity. As discussed in [20,50], this is a good approximation for sufficiently early times; π perturbations give a negligible contribution to the observable quantity ζ, while χ perturbations will source ζ by one of the standard conversion mechanisms.…”

Scale-invariant fluctuations from Galilean genesis

“…This mass will induce non-trivial dynamics of φ which in turn leads to a linear coupling between fluctuations in φ and curvature perturbations. Alternatively, we could also consider a gravitational action with induced non-minimal coupling of φ to gravity (a similar mechanism was proposed in [11]): This modified action also leads to a direct linear coupling between fluctuations of φ and curvature perturbations. For definiteness, in the present work, we only consider the first possibility, which is inspired by a Kähler potential in supersymmetry 1 .…”

“…Recently, there is an increasing interest in a class of alternatives to inflation in which the scale-invariance of the fluctuations is induced not by the de-Sitter-like expansion of space, but by the evolution of another matter field. Examples are the conformal cosmology of [8] (see also [9][10][11]), in which the evolution of a conformal scalar field induces scale-invariant fluctuations in an axion-like field to which it couples, the pseudo-conformal cosmology of [12] and the Galilean genesis model of [1] in which a Galileon field which dominates the background dynamics of space-time induces scale-invariant fluctuations of a spectator scalar fields.…”

Towards conformal cosmology

“…This option has been studied in Ref. [33]. It has been shown that mixing of the scalar field(s) with the metric in dynamical pseudo-conformal models does not introduce new strong-coupling UV scales.…”