Scalar Field Perturbations with Arbitrary Potentials in Quantum Backgrounds

TL;DR

This paper develops a new method to derive a second order Hamiltonian for quantum scalar perturbations with arbitrary potentials, without relying on classical background equations, enabling better analysis of quantum cosmological evolution.

Contribution

It introduces a novel approach using the Faddeev-Jackiw procedure to obtain Hamiltonians for scalar perturbations with arbitrary potentials and hypersurfaces, generalizing previous models.

Findings

Derived a general second order Hamiltonian for scalar perturbations

Enabled analysis without classical background equations

Applicable to arbitrary potentials and spacelike hypersurfaces

Abstract

In this paper it is shown how to obtain, without ever using the background classical equations of motion, a simple second order Hamiltonian involving the Mukhanov-Sasaki variable describing quantum linear scalar perturbations for the case of scalar fields with arbitrary potentials and arbitrary spacelike hyper-surfaces. It is a generalization of previous works, where the scalar field potential was absent and the spacelike hypersurfaces were flat. This was possible due to the implementation of a new method, together with the Faddeev-Jackiw procedure for the constraint reduction. The resulting Hamiltonian can then be used to study the evolution of quantum cosmological perturbations in quantum backgrounds.