Quantum Phase Space Description of a Cosmological Minimal Massive Bigravity Model

TL;DR

This paper applies deformation quantization to a ghost-free bimetric gravity cosmological model, analyzing quantum states via Wigner functions and revealing a connection between graviton mass and cosmological constant.

Contribution

It introduces a novel quantum cosmology approach for the Hassan-Rosen bigravity model using deformation quantization and explores the graviton mass as an emergent cosmological constant.

Findings

Wigner functions computed for different wavefunctions, including analytical results for Hartle-Hawking.

Graviton mass interpreted as an emergent cosmological constant and deviation measure.

Relation between curvature and graviton mass on a cusp catastrophe surface.

Abstract

Bimetric gravity theories describes gravitational interactions in the presence of an extra spin-2 field. The Hassan-Rosen (HR) nonlinear massive minimal bigravity theory is a ghost-free bimetric theory formulated with respect a flat, dynamical reference metric. In this work the deformation quantization formalism is applied to a HR cosmological model in the minisuperspace. The quantization procedure is performed explicitly for quantum cosmology in the minisuperspace. The Friedmann-Lema\^itre-Robertson-Walker (FLRW) model with flat metrics is worked out and the computation of the Wigner functions for theHartle-Hawking, Vilenkin and Linde wavefunctions are done numerically and, in the Hartle-Hawking case, also analytically. From the stability analysis in the quantum minisuper phase space it is found an interpretation of the mass of graviton as an emergent cosmological constant and as a measure of the deviation of classical behavior of the Wigner functions. Also, from the Hartle-Hawking case, an interesting relation between the curvature and the mass of graviton in a cusp catastrophe surface is discussed