Scalar Perturbations in Scalar Field Quantum Cosmology

Abstract

In this paper it is shown how to obtain the simplest equations for the Mukhanov-Sasaki variables describing quantum linear scalar perturbations in the case of scalar fields without potential term. This was done through the implementation of canonical transformations at the classical level, and unitary transformations at the quantum level, without ever using any classical background equation, and it completes the simplification initiated in investigations by Langlois [2], and Pinho and Pinto-Neto [4] for this case. These equations were then used to calculate the spectrum index ns of quantum scalar perturbations of a non-singular inflationary quantum background model, which starts at infinity past from flat space-time with Planckian size spacelike hypersurfaces, and inflates due to a quantum cosmological effect, until it makes an analytical graceful exit from this inflationary epoch to a decelerated classical stiff matter expansion phase. The result is ns = 3, incompatible with observations.

A Momentous Arrow of Time

“…[39,40,41,42,43,44,45]. For linear perturbations, moreover, topological properties of solution spaces mostly disappear such that a reduced quantization here may be viable [46,47]. Alas, it cannot present a full theory if it is simply added on to the bouncing background as treated so far, which was by the Dirac rather than the reduced phase space procedure.…”

Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase-space — A review and applications

“…A formulation of cosmological perturbation theory in the framework of the relational formalism based on the reduced phase space in terms of Ashtekar variables can be found in [29]. For other examples where cosmological perturbation theory has been analyzed in the canonical framework see for instance [30,31].…”

Benefits of Objective Collapse Models for Cosmology and Quantum Gravity

“…In fact, some work in these directions has been done already. For instance, applications of dBB to cosmology include [16,52,51,44,45,19], and, in particular, in [16,52,51] it is argued that, at least in the cosmological setting, one might question the validity of the equilibrium prescription for the initial dBB distribution (of course not all works which apply dBB to cosmology share this non-equilibrium assumption). Such out-of-equilibrium proposal is based on cosmological considerations, like the fact that we do not have access to an ensemble of universes.…”