More on "Little Lambda" in Ho\v{r}ava-Lifshitz Gravity

TL;DR

This paper investigates the role of the coupling constant lambda in lambda-R models inspired by Horava-Lifshitz gravity, clarifying its impact on the equivalence to general relativity and resolving previous contradictions.

Contribution

It provides a detailed canonical analysis of lambda-R models with closed boundaries, reconciling earlier conflicting results about their physical significance.

Findings

All non-projectable lambda-R models are equivalent to general relativity in asymptotically flat cases.

The tertiary constraint for closed boundaries has a more general form than previously thought.

The analysis resolves contradictions regarding the physical relevance of lambda in cosmological contexts.

Abstract

We analyze different claims on the role of the coupling constant lambda in so-called lambda-R models, a minimal generalization of general relativity inspired by Horava-Lifshitz gravity. The dimensionless parameter lambda appears in the kinetic term of the Einstein-Hilbert action, leading to a one-parameter family of classical theories. Performing a canonical constraint analysis for closed spatial hypersurfaces, we obtain a result analogous to that of Bellorin and Restuccia, who showed that all non-projectable lambda-R models are equivalent to general relativity in the asymptotically flat case. However, the tertiary constraint present for closed boundary conditions assumes a more general form. We juxtapose this with an earlier finding by Giulini and Kiefer, who ruled out a range of lambda-R models by a physical, cosmological argument. We show that their analysis can be interpreted consistently within the projectable sector of Horava-Lifshitz gravity, thus resolving the apparent contradiction.