The cosmological constant as an eigenvalue of the Hamiltonian constraint in Horava-Lifshits theory

TL;DR

This paper investigates the cosmological constant as an eigenvalue in the Wheeler-DeWitt equation within Horava-Lifshitz gravity, using a variational approach to analyze vacuum states and eigenvalues.

Contribution

It introduces a method to compute the cosmological constant as an eigenvalue in Horava-Lifshitz theory, considering both detailed balanced and non-balanced cases.

Findings

Eigenvalues depend on coupling constants and physical scale.

Existence of eigenvalues varies with detailed balance condition.

Variational method effectively computes vacuum expectation values.

Abstract

In the framework of Horava-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.