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.
Highlights
Since 1916, Einstein’s general relativity theory (GR) [1] has explained the majority of the phenomena related to gravity
Where N (t) and M (t) are the lapse functions, a(t) and b(t) are the scale factors of metrics gμν and fμν, respectively, and K is the space curvature which is assumed to be the same for both metrics [57, 58]. Upon substitution of these metric coefficients and the definitions of Ricci scalars into the equations (3) and (4), besides the simplification assumption Mg2 = Mf2 = Me2ff /2, we can obtain a point-like form for the gravitational Lagrangian in the minisuperspace {N, a, M, b} as aa 2 N
Using the Hamiltonian formalism for bigravity theory we have studied the classical and quantum cosmological behaviors of the particular massive bigravity model so called minimal bigravity
Summary
Since 1916, Einstein’s general relativity theory (GR) [1] has explained the majority of the phenomena related to gravity. Later in 1987, the Coleman-De Luccia instanton was discovered to overcome the limitation of only having closed spatial three-geometries [42] They showed that the false vacuum decay proceeds via the nucleation of bubbles whose interior is an infinite open universe in which inflation may occur. There are plenty of interesting quantum cosmological models for flat and open universes in which rather than focusing on the closed universes and calculating the “creation from nothing” probability, the Wheeler-DeWitt equation is obtained for flat or open universe and those solutions of WheelerDeWitt equation are taken with the criteria of just having good asymptotic behaviour in minisuperspace giving rise to normalizable states or wave-packets [49]. A relevant work to the present paper has been recently reported [50] in which the quantum cosmology for the open FRW universe was studied based on the Hamiltonian formalism for massive gravity theory and the corresponding wave packet solutions were obtained.
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