Bouncing and cyclic quantum primordial universes and the ordering problem

Abstract

In a Bohmian quantum cosmology scenario, we investigate some quantum effects on the evolution of the primordial universe arising from the adoption of an alternative non-trivial ordering to the quantization of the constrained Hamiltonian of a minimally coupled scalar field. The Wheeler-DeWitt equation has a contribution from the change in factor ordering, hence there are new quantum effects. We compare the results between the non-trivial and the trivial ordering cases, showing that the classical limit is valid for both orderings, but new bouncing and cyclic solutions are present in the non-trivial case. Additionally, we show that the non-singular solutions already present in the trivial ordering formalism keep valid. * Bohmian) quantum cosmology. In Refs. [7-9], it is described how such an alternative interpretation can be generalized from quantum mechanics to cosmological models such as those of Eq. (1). In particular, even when V = 0 one is able to solve the singularity problem thanks to quantum corrections, which induce a bounce. The case of an exponential potential, related with a matter-dominated universe, was recently presented in Ref. [10].The Lagrangian (1) can also be seen as one of the simplest particular cases of Horndeski modified gravity theory [11], thus it is free of Ostrogradsky instability [12,13]. It is also in agreement with the recent constraints imposed by GW170817 and GRB170817A [14-16] on the velocity of gravitational waves. See e.g. Ref.[13]. Lagrangian (1) is also related with effective string theory [7] and is also the Einstein frame version of several other scalar-tensor theories of gravity [5].The motivation for adopting an alternative interpretation of quantum mechanics in a cosmological setting comes from the fact that the exterior domain hypothesis [17], tacitly present in most standard interpretations of quantum mechanics, is considered by some authors as being a conceptual problem when the system under investigation is the universe [18][19][20]. Because of that, it has been proposed [20-23] to adopt in cosmology the Bohmian interpretation of quantum mechanics [24,25]. Besides that, the Bohmian interpretation also solves the problem of time ambiguity in quantum cosmology and quantum gravity [26,27], thanks to the guidance equations. More about Bohm-de Broglie quantum mechanics can be found in Refs. [28][29][30][31][32][33].Another conceptual problem faced in the quantisation of a gravitational theory like (1) is the factor ordering ambiguity, a direct consequence of Dirac's quantisation rule. In Ref. [23], it is shown that the basic features of Bohmian quantum gravity do not really depend on the factor ordering, although some ordering must be chosen to actually apply quantisation. Basead on that argument, it is common to apply only the trivial ordering in the quantization of the constrained Hamiltonian, like it is done in Ref. [23]. But the factor ordering ambiguity remains, so that we can ask ourselves: if the general features of that theory are invariant under a change of ordering...

Cosmological bouncing solutions in f(T, B) gravity

“…These effective theories of gravity offer qualitatively similar results indicating a potential universality of this type of bounce scenario. Another interesting proposal for potential bounce cosmologies is that of an oscillatory, or cyclic, bounce [4,29,30] where a regular periodic bounce occurs at finite temporal intervals, and may offer an new avenue to resolving cosmological problems in the early universe [31,32]. The differences between these bouncing scenarios can also be viewed through the lens of Fig.1 where the fundamental cosmological parameters are plotted for each bounce model.…”