Scalar fields and 3D Flat Space Cosmologies

TL;DR

This paper investigates scalar perturbations and quasi-normal modes in 3D flat space cosmologies, linking them to BTZ black holes, and uses these to compute the scalar one-loop partition function.

Contribution

It provides a detailed analysis of scalar QNMs in 3D FSCs, extending the flat space limit of BTZ black hole results, and constructs the scalar one-loop partition function.

Findings

QNMs treated as complex momenta with a cosmological horizon as a hard wall

Connection established between FSC QNMs and BTZ black hole analysis

Scalar one-loop partition function computed and compared with literature

Abstract

Flat Space Cosmologies (FSC) are time-dependent solutions in Einstein gravity in three-dimensional (3D) spacetimes with zero cosmological constant. These are orbifolds of 3D flat space that have a cosmological horizon and can be thought of as analogs of the Banados-Tietelboim-Zanelli (BTZ) black holes of AdS$_3$. We study scalar perturbations about these FSC solutions and explore the spectrum of quasi-normal modes (QNMs) crucially treating the cosmological horizon as a hard wall and extending to complex momenta. We connect this intrinsic analysis with the flatspace limit of the corresponding analysis in the BTZ black hole. The FSC QNMs are then utilized to build the scalar one-loop partition function by methods pioneered by Denef, Hartnoll and Sachdev in various simplifying limits and compared with existing answers in the literature.