Scalar Perturbations in Scalar Field Quantum Cosmology

TL;DR

This paper derives simplified equations for quantum scalar perturbations in scalar field cosmology without potential, and calculates their spectral index, finding it incompatible with observational data.

Contribution

It introduces a novel method using canonical and unitary transformations to simplify perturbation equations without classical background equations, applied to a quantum cosmological inflation model.

Findings

Derived simplified equations for scalar perturbations

Calculated spectral index n_s=3 for a quantum inflation model

Found the spectral index incompatible with observations

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 \cite{langlois}, and Pinho and Pinto-Neto \cite{emanuel2} for this case. These equations were then used to calculate the spectrum index $n_s$ 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 $n_s=3$, incompatible with observations.