Hořava-Lifshitz Quantum Cosmology

Abstract

In this work, a minisuperspace 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 HL gravity, there is a "potential barrier" nearby $a=0$. For a vanishing cosmological constant, it is found a normalizable wave function of the universe. When the cosmological constant is non-vanishing, the WKB method is used to obtain solutions for the wave function of the universe. Using the Hamilton-Jacobi equation, one discusses how the transition from quantum to classical regime occurs and, for the case of a positive cosmological constant, the scale factor is shown to grow exponentially, hence recovering the GR behaviour for the late universe.

27 pages, 7 figures

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• Classical and statistical limits of the quantum singular oscillator
• Generalized Uncertainty Principle effects in the Hořava-Lifshitz quantum theory of gravity
• Quantum Hořava-Lifshitz cosmology in the de Broglie-Bohm interpretation
• Resolution of cosmological singularity in Hořava-Lifshitz cosmology
• Euclidean Wormholes in Horava-Lifshitz Gravity
• Dark energy and normalization of cosmological wave function in modified gravitations
• Hořava-Lifshitz $F(\bar{R})$ theories and the Swampland
• Lorentzian Vacuum Transitions in Hořava-Lifshitz Gravity
• On the energy flow of $\lambda$ in Hořava-Lifshitz cosmology