Quantum Cosmological Perturbations of Generic Fluids in Quantum Universes

TL;DR

This paper extends previous methods to derive simplified Hamiltonians for cosmological perturbations in universes with generic fluids, including entropy perturbations, using a novel approach that avoids classical background equations.

Contribution

It introduces a new method with the Faddeev-Jackiw procedure to generalize Hamiltonian formulations to arbitrary fluids and spacelike hyper-surfaces in quantum cosmology.

Findings

Derived a simple second order Hamiltonian involving the Mukhanov-Sasaki variable.

Generalized previous results to include entropy perturbations.

Avoided using background classical equations of motion in the derivation.

Abstract

In previous works, it was shown that the Lagrangians and Hamiltonians of cosmological linear scalar, vector and tensor perturbations of homogeneous and isotropic space-times with flat spatial sections containing a perfect fluid can be put in a simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. In this paper, we generalize this result to general fluids, which includes entropy perturbations, and to arbitrary spacelike hyper-surfaces through a new method together with the Faddeev-Jackiw procedure for the constraint reduction. A simple second order Hamiltonian involving the Mukhanov-Sasaki variable is obtained, again without ever using the background equations of motion.