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

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.