BRST Quantization of Cosmological Perturbations

TL;DR

This paper explores BRST and Dirac quantization methods for cosmological perturbations in scalar field dominated universes, emphasizing gauge-invariant calculations and simplifying propagator structures.

Contribution

It applies Hamiltonian BRST and Dirac quantization to cosmological perturbations in a time-dependent background, highlighting gauge choices and simplifications for free theories.

Findings

BRST quantization simplifies propagator structures in derivative gauges

Dirac quantization in synchronous gauge avoids ghosts and maintains locality

Canonical transformations diagonalize the free Hamiltonian

Abstract

BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to the perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structure of the propagators, whereas quantization in synchronous gauge, which amounts to Dirac quantization, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.