Vacuum Persistence in Fierz-Pauli Theory on a Curved Background

TL;DR

This paper investigates how the Higuchi bound for a free spin-2 field on curved backgrounds is modified when additional symmetry-allowed terms are included, with implications for cosmological models like FRW universes.

Contribution

It extends the Higuchi bound by incorporating additional terms in the vacuum persistence amplitude, providing a generalized bound applicable to maximally symmetric spacetimes.

Findings

The Higuchi bound is modified by additional symmetry-allowed terms.

The generalized bound applies to maximally symmetric spacetimes such as FRW universe.

Implications for stability conditions of spin-2 fields in cosmological backgrounds.

Abstract

By explicitly constructing the Hilbert space, Higuchi showed that there is a lower bound on the mass of a minimally-coupled free spin-2 field on a curved background \cite{HiguchiBound}. Using the vacuum persistence amplitude, we show that this bound is modified by taking into account additional terms not prohibited by symmetry in the case of a maximally symmetric spacetime. This result can further be generalized to the maximally symmetric space case, such as the FRW universe, and its corresponding bound of the deformation parameter is discussed.