Classical and quantum cosmology of Born-Infeld type models

Abstract

We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equation was previously found in the quantization of black holes. We give explicit results for the cases of constant potential and inverse squared potential and point out special features possessed by solutions of the difference equation.

On the dynamics of the general Bianchi IX spacetime near the singularity

“…Although a theory of quantum gravity is not yet available in finite form, various approaches exist within which the question of singularity avoidance can be addressed [2]. Quantum cosmological examples for such an avoidance can be found, for example, in [3][4][5][6] and the references therein.…”

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

“…the ones remaining after an appropriate choice of a gauge fixing condition. This approach was put in action in [4] and more recently in [5]; the first work has an overlap with the present work in the case of FLRW cosmology. As we explicitly show in the appendix B, the wave functions we find are identical to the ones in [4], even though we take a different tributary from the same river.…”

Phantom singularities and their quantum fate: general relativity and beyond—a CANTATA COST action topic

“…Type II A sudden singularity takes place at finite cosmic time with finite scale factor, where the Hubble parameter remains finite but its cosmic time derivative diverges [54,62,63,64]. It is also known as a big brake [64,65,66] if it takes place in the future with an infinite deceleration or a big démarrage [67], named also big boost [68], if it happens in the past with an infinite acceleration. The latter case is realized by a generalized Chaplygin gas [67,69], see also section 4.2.2 below.…”