Primordial dust universe in the Ho\v{r}ava-Lifshitz theory

Abstract

We apply quantum cosmology to investigate the early moments of a Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological model, using Ho\v{r}ava-Lifshitz (HL) as the gravitational theory. The matter content of the model is a dust perfect fluid. We start studying the classical model. Then, we write the total Hamiltonian of the model, quantize it and find the appropriate Wheeler-DeWitt equation. In order to avoid factor ordering ambiguities, in the Wheeler-DeWitt equation, we introduce a canonical transformation. We solve that equation using the Wentzel-Kramers-Brillouin (WKB) approximation and compute the tunneling probabilities for the birth of that universe ($TP_{WKB}$). Since the WKB wavefunction depends on the dust energy and the free coupling constants coming from the HL theory, we compute the behavior of $TP_{WKB}$ as a function of all these quantities.