Quantum singularities in Hořava-Lifshitz cosmology

The recently proposed Hořava-Lifshitz theory of gravity is analyzed from the quantum cosmology point of view. By employing usual quantum cosmology techniques, we study the quantum Friedmann-Lemaître-Robertson-Walker universe filled with radiation in the context of Hořava-Lifshitz gravity. We find that this universe is quantum mechanically nonsingular in two different ways: the expectation value of the scale factor $⟨a⟩(t)$ never vanishes and, if we abandon the detailed balance condition suggested by Hořava, the quantum dynamics of the universe is uniquely determined by the initial wave packet and no boundary condition at $a=0$ is necessary.

Figure 1

The evolution of the scale factor in the case of an attractive potential. Twenty terms in the expansion Eq. (63) were used in this numerical approximation.