Abstract
In this paper, we study a projectable Hořava-Lifshitz cosmology without the detailed balance condition minimally coupled to a nonlinear self-coupling scalar field. In the minisuperspace framework, the super-Hamiltonian of the presented model is constructed by means of which some classical solutions for the scale factor and scalar field are obtained. Since these solutions exhibit various types of singularities, we came up with the quantization of the model in the context of the Wheeler-DeWitt approach of quantum cosmology. The resulting quantum wave functions are then used to investigate the possibility of the avoidance of classical singularities due to quantum effects which show themselves important near these singularities.
Highlights
A new gravitation theory based on anisotropic scaling of the space x and time t was presented by Hořava
Some of these are as follows: [16], in which a projectable Uð1Þ symmetric soft-breaking detailed balance condition model is considered and it is shown that the resulting theory displays anisotropic scaling at short distances while almost all features of general relativity (GR) are recovered at long distances
The phase space variables turn out to correspond to the scale factor of the FRW metric and a nonlinear self-coupling scalar field with which the action of the model is augmented
Summary
A new gravitation theory based on anisotropic scaling of the space x and time t was presented by Hořava. It is worth noting that almost all physically important solutions of the Einstein equations like Schwarzschild, Reissner-Nordström, Kerr, and Friedmann-Lemaitre-Robertson-Walker space times can be cast into the projectable form by suitable choice of coordinates, most of the results, in principle, may be extended to the nonprojectable case through a challenging but straightforward calculation [13, 14] Another thing to note about the HL theory is the form of its action which in general consists of two kinetic and potential terms. There are some extensions of the initial version of the HL gravity theory that deal with such problems Some of these are as follows: [16], in which a projectable Uð1Þ symmetric soft-breaking detailed balance condition model is considered and it is shown that the resulting theory displays anisotropic scaling at short distances while almost all features of GR are recovered at long distances. Theory to see how things may change their behavior if the quantum mechanical considerations come into the model
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