Classical and quantum cosmology of minimal massive bigravity

TL;DR

This paper explores classical and quantum cosmological models within minimal massive bigravity, revealing how massive gravitons influence universe evolution and how quantum effects can resolve classical singularities.

Contribution

It introduces the classical and quantum cosmological equations for minimal massive bigravity, including exact solutions and the avoidance of initial singularities via quantum cosmology.

Findings

Massive graviton acts as a cosmological term affecting universe dynamics

Quantum cosmology solutions suggest initial singularity avoidance

Graviton mass is large at early universe, consistent with large cosmological constant

Abstract

In a Friedmann-Robertson-Walker (FRW) space-time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the classical field equations acquire contribution from the massive graviton as a cosmological term which is positive or negative depending on the dynamical competition between two scale factors of bigravity metrics. We obtain the classical field equations for flat and open universes in the ordinary and Schutz representation of perfect fluid. Focusing on the Schutz representation for flat universe, we find classical solutions exhibiting singularities at early universe with vacuum equation of state. Then, in the Schutz representation, we study the quantum cosmology for flat universe and derive the Schrodinger-Wheeler-DeWitt equation. We find its exact and wave packet solutions and discuss on their properties to show that the initial singularity in the classical solutions can be avoided by quantum cosmology. Similar to the study of Hartle-Hawking no-boundary proposal in the quantum cosmology of de Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass of graviton predicted by quantum cosmology of the minimal massive bigravity is large at early universe. This is in agreement with the fact that at early universe the cosmological constant should be large.