Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

TL;DR

This paper derives the Berry phase for primordial scalar and tensor perturbations during single-field inflation, providing a new perspective on quantum phases in early universe cosmology.

Contribution

It introduces a method to calculate the adiabatic Berry phase for inflationary perturbations using invariant operators, resolving previous discrepancies in the literature.

Findings

Derived Hamiltonians as time-dependent harmonic oscillators

Calculated the Berry phase for sub-horizon modes

Resolved discrepancies in prior Berry phase calculations

Abstract

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis-Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et. al [Class. Quant. Grav. 30 (2013) 12] for these Berry phases, which is resolved to yield agreement with our results.