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Quantum phase space description of a cosmological minimal massive bigravity model

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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–Lemaître–Robertson–Walker model with flat metrics is worked out and the computation of the Wigner functions for the Hartle–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.

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Acknowledgements

The author want to thank the referee for the comments and suggestions which allowed to improve this work. The author is indebted to Rubèn Cordero and Marta Costa for all his help and fruitful discussions.

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Vera-Hernández, J.C. Quantum phase space description of a cosmological minimal massive bigravity model. Gen Relativ Gravit 53, 55 (2021). https://doi.org/10.1007/s10714-021-02822-2

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