Ho·rava-Lifshitz quantum cosmology

Full text: In this poster, a mini-superspace model for the projectable Hořava-Lifshitz (HL) gravity without the detailed balance condition is investigated. The Wheeler-DeWitt equation is derived and its solutions are studied and discussed for some particular cases where, due to Hofava-Lifshitz gravity, there is a 'potential barrier' nearby a = 0. The solutions for the WdW equation are obtained considering the deWitt boundary condition which states that the wave function vanishes at the singularity. For a ≪ 1, corresponding to the very early universe when the HL gravity terms dominate, the wave function is an exponential, that is typical of classically forbidden region. A quantum bound for the coefficient gs is found. For the very late universe, when a ≫ 1, the curvature and the cosmological constant terms dominate and, one finds that, for Λ = 0 or Λ < 0, the wave function is exponentially suppressed, denoting as before, that this region is classically forbidden. For a positive cosmological constant case, one finds a damped oscillatory behaviour, already found in the usual Quantum Cosmology for General Relativity For the vanishing cosmological constant, an exact solution can be obtained. In this case, one find s that the singularity is avoided due to quantum effects as the probability to reach the singularity a = 0 vanishes and that gr is quantized. Fixing the value of gs, for large values of n (large gr values), one can obtain a classical universe according to the analog of the correspondence principle of old quantum mechanics. The complete exact solution for Λ ≠ 0 cannot be obtained, although wave functions in the WKB approximation can be obtained for the intermediate regions. Finally, the discussion on how the classical solution emerges from the semiclassical analysis is performed solving the Hamilton-Jacobi equation: one encounters a semiclassical solution oscillating nearby the classical solution. For Λ > 0 and a ≫ 1, this leads to a de Sitter space-time, as expected from general relativity. One then concludes that quantum cosmology applied to Hofava-Lifshitz gravity suggests that this proposal matches the expectations of a quantum gravity model for the very early universe, as it provides, for instance, a hint for the singularity problem for the Λ = 0 case. In what concerns specific solutions, the model suggests that GR behaviour is recovered at the semiclassical limit. (author)