A generalized Selberg zeta function for flat space cosmologies

TL;DR

This paper introduces a generalized Selberg zeta function for flat space cosmologies, linking it to 1-loop partition functions and providing a new method for calculating quantum corrections in 3D gravity.

Contribution

It develops a novel Selberg zeta function for FSCs and extends the formalism to general quotient manifolds, offering an efficient way to compute 1-loop determinants without heat kernel methods.

Findings

Derived a new Selberg zeta function for FSCs

Connected the zeta function to scalar 1-loop partition functions

Matched quasinormal modes to known results

Abstract

Flat space cosmologies (FSCs) are time dependent solutions of three-dimensional (3D) gravity with a vanishing cosmological constant. They can be constructed from a discrete quotient of empty 3D flat spacetime and are also called shifted-boost orbifolds. Using this quotient structure, we build a new and generalized Selberg zeta function for FSCs, and show that it is directly related to the scalar 1-loop partition function. We then propose an extension of this formalism applicable to more general quotient manifolds $\mathcal M/\mathbb Z$, based on representation theory of fields propagating on this background. Our prescription constitutes a novel and expedient method for calculating regularized 1-loop determinants, without resorting to the heat kernel. We compute quasinormal modes in the FSC using the zeroes of a Selberg zeta function, and match them to known results.