The Cosmological Constant in Distorted Quantum Cosmology

TL;DR

This paper proposes a novel method to compute the cosmological constant using the Wheeler-DeWitt equation, considering deviations from General Relativity through frameworks like Gravity's Rainbow and Noncommutative geometry.

Contribution

It introduces a calculation scheme treating the cosmological constant as an eigenvalue in a Sturm-Liouville problem within distorted quantum cosmology.

Findings

Applied the scheme to Gravity's Rainbow and Noncommutative geometry.

Provided insights into the effects of deviations from General Relativity on the cosmological constant.

Discussed potential implications for Hořava-Lifshitz theory.

Abstract

We give a calculation scheme for the cosmological constant computation with the help of the Wheeler-DeWitt equation. This last one is regarded as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. By fixing the ideas on a Friedmann-Lema\^{\i}tre-Robertson-Walker line element in ordinary gravity, we apply this calculation scheme on distorted gravity. By distorted gravity, we mean all the deviations from General Relativity. We restrict our proposal on Gravity's Rainbow and Noncommutative geometry. A brief comment on Ho\v{r}ava-Lifshitz (HL) theory is discussed.