Cosmological constant as an eigenvalue of the Hamiltonian constraint in Horava-Lifshitz theory

In the framework of Hořava-Lifshitz theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. The explicit calculation is performed with the help of a variational procedure with trial wave functionals of the Gaussian type. We analyze both the case with the detailed balanced condition and the case without it. In the case without the detailed balance, we find the existence of an eigenvalue depending on the set of coupling constants (g2, g3) and (g4, g5, g6), respectively, and on the physical scale.