Primordial dust universe in the Hořava–Lifshitz theory

Abstract

In this paper, we apply quantum cosmology to investigate the early moments of a Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model, using Hořava–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 ([Formula: see text]). Since the WKB wave function depends on the dust energy and the free coupling constants coming from the HL theory, we compute the behavior of [Formula: see text] as a function of all these quantities.