# The Cosmological Constant and Horava-Lifshitz Gravity

## TL;DR

This paper explores how Horava-Lifshitz gravity can be reconciled with the observed small cosmological constant by considering vacuum energy effects, linking the smallness of the cosmological constant to Lorentz invariance breaking at tiny scales.

## Contribution

It proposes a mechanism to approximately compensate the negative bare cosmological constant in Horava-Lifshitz gravity using quantum vacuum energy effects, relating it to Lorentz invariance breaking scales.

## Key findings

- The scale of Lorentz invariance breaking is about 5 times the Planck length for a near-zero cosmological constant.
- A relation between the smallness of the cosmological constant and the scale of dimension 4 corrections is established.
- First rough estimates for the infrared parameters $$ and $_w$ are provided.

## Abstract

Horava-Lifshitz theory of gravity with detailed balance is plagued by the presence of a negative bare (or geometrical) cosmological constant which makes its cosmology clash with observations. We argue that adding the effects of the large vacuum energy of quantum matter fields, this bare cosmological constant can be approximately compensated to account for the small observed (total) cosmological constant. Even though we cannot address the fine-tuning problem in this way, we are able to establish a relation between the smallness of observed cosmological constant and the length scale at which dimension 4 corrections to the Einstein gravity become significant for cosmology. This scale turns out to be approximately 5 times the Planck length for an (almost) vanishing observed cosmological constant and we therefore argue that its smallness guarantees that Lorentz invariance is broken only at very small scales. We are also able to provide a first rough estimation for the infrared values of the parameters of the theory $\mu$ and $Lambda_w$.