Scalar-metric quantum cosmology with Chaplygin gas and perfect fluid

Abstract

In this paper we consider the flat FRW cosmology with a scalar field coupled with the metric along with generalized Chaplygin gas and perfect fluid comprising the matter sector. We use the Schutz's formalism to deal with the generalized Chaplygin gas sector. The full theory is then quantized canonically using the Wheeler-DeWitt Hamiltonian formalism. We then solve the WD equation with appropriate boundary conditions. Then by defining a proper completeness relation for the self-adjointness of the WD equation we arrive at the wave packet for the universe. It is observed that the peak in the probability density gets affected due to both fluids in the matter sector, namely, the Chaplygin gas and perfect fluid.

Anisotropic scalar-metric quantum cosmology and unitarity

“…This is a feature which has been observed in the literature for anisotropic cosmological models and appears in our analysis also. In this regard we would like to point out that such a nonunitary quantum evolution of the universe was also seen in [23] for FRW metric which is an isotropic cosmological model. This actually owed its origin to the inclusion of the scalar field in the model.…”

“…To construct a well behaved wave function, we now need to discuss about the appropriate boundary conditions. To do that, we take note of the fact that for the operator Ĥ to be a self-adjoint operator, one should define the inner product between any two wave functions Φ 1 and Φ 2 in the following way [23] (…”

“…The role of time is played by the monotonic evolution of the fluid density. However, the Chaplygin gas model has also been used as the matter sector in many studies [21]- [23]. The reason for using the Chaplygin gas model is due to its ability to describe the accelerating stage of the universe [24,25].…”

“…In this paper, we investigate the quantum cosmology of a scalar field coupled to an anisotropic Bianchi I spacetime in the presence of a perfect fluid. The motivation of carrying out this analysis is that such an analysis has been carried out in [23] in the case of a flat FRW spacetime which is an isotropic model. However, one may argue that it is not certain whether the observed universe is isotropic at very early stages of its evolution.…”

“…Therefore, carrying out a similar analysis in an anisotropic cosmological scenario seems to be essential. The reason for introducing the scalar field in the model (as was done in our previous paper [23]) is to explore its effect on the evolution of the universe. Such a curiosity is worthwhile in its own right since it is quite plausible that the evolution of the universe at very early stages could get affected by such fields.…”