Nonperturbative quantum dynamics of a new inflation model

Abstract

We consider an O(N) model coupled self-consistently to gravity in the semiclassical approximation, where the field is subject to ''new inflation'' type initial conditions. We study the dynamics self-consistently and non-perturbatively with non-equilibrium field theory methods in the large N limit. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off the inflationary growth of the scale factor. We find that a very specific combination of these large fluctuations plus the inflaton zero mode assemble into a new effective field. This new field behaves classically and it is the object which actually rolls down. We show how this reinterpretation saves the standard picture of how metric perturbations are generated during inflation and that the spinodal growth of fluctuations dominates the time dependence of the Bardeen variable for superhorizon modes during inflation. We compute the amplitude and index for the spectrum of scalar density and tensor perturbations and argue that in all models of this type the spinodal instabilities are responsible for a ''red'' spectrum of primordial scalar density perturbations. A criterion for the validity of these models is provided and contact with the reconstruction program is established validating some of the results within a non-perturbative framework. The decoherence aspects and the quantum to classical transition through inflation are studied in detail by following the full evolution of the density matrix and relating the classicality of cosmological perturbations to that of long-wavelength matter fluctuations.

Phase transitions in the early and the present Universe: from the big bang to heavy ion collisions

“…The picture that emerges from this brief tour through the early Universe, is that while current CMB measurements and large scale surveys have the potential for revealing evidence for inflationary phase transitions the observable evidence for a standard model phase transition is at best indirect. I have argued that inflationary phase transitions, perhaps taking place at the GUT scale could leave an imprint in the power spectrum of temperature anisotropies, for example a red tilt as a consequence of spinodal instabilities [9]. Or as argued in ref.…”

“…We refer the reader to ref. [8,9,12] for more details which fall outside the main scope of these lectures.…”

“…While the evolution of the scale factor along with the dynamics of the scalar field (inflaton) were typically studied using the classical equations of motion for the scalar field, more recently a consistent description of the quantum dynamics has been provided [8,9,12]. The non-equilibrium dynamics of cosmological phase transitions requires a non-perturbative framework that treats self-consistently the dynamics of the matter field and the evolution of the metric.…”

“…the coefficients A k , B k are determined by initial conditions [9]. When the physical wavevector crosses the horizon, i.e, when k e −Ht ≪ H the solution grows exponentially and is given by…”

“…Thus the exponential growth of superhorizon fluctuations given by (3.14) is a direct consequence of the spinodal instabilities associated with the phase transition during the De Sitter inflationary epoch. A detailed calculation of the power spectrum of density fluctuations [9,11] yields…”