The initial moments of a Hořava-Lifshitz cosmological model

Abstract

In the present work, we study the initial moments of a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model, considering Hořava-Lifshitz (HL) as the gravitational theory. The matter content of the model is a radiation perfect fluid. In order to study the initial moments of the universe in the present model, we consider quantum cosmology. More precisely the quantum mechanical tunneling mechanism. In that mechanism, the universe appears after the wavefunction associated to that universe tunnels through a potential barrier. We started studying the classical model. We draw the phase portrait of the model and identify qualitatively all types of dynamical behaviors associated to it. Then, we write the Hamiltonian of the model and apply the Dirac quantization procedure to quantize a constrained theory. We find the appropriate Wheeler-DeWitt equation and solve it using the Wentzel-Kramers-Brillouin (WKB) approximation. Using the WKB solution, to the Wheeler-DeWitt equation, we compute the tunneling probabilities for the birth of that universe (\(TP_{WKB}\)). Since the WKB wavefunction depends on the radiation energy (E) and the free parameters coming from the HL theory (\(g_c\), \(g_r\), \(g_s\), \(g_\Lambda \)), we compute the behavior of \(TP_{WKB}\) as a function of E and all the HL’s parameters \(g_c\), \(g_r\), \(g_s\), \(g_\Lambda \). As a new result, due to the HL theory, we notice that, in the present model, the universe cannot tunnel through the barrier close to the origin. It happens because that tunneling probability is nil. Therefore, here, the universe cannot starts from a zero size and is free from the big bang singularity.