The cosmological constant and Horava-Lifshitz gravity

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 Lambda(OBS), thus resulting in a self-contained model of gravity and particle physics. Even though we cannot address the fine-tuning problem in this way, we are able to establish a relation between the smallness of Lambda(OBS) and the scale l(UV) at which dimension 4 corrections to the Einstein gravity become significant for cosmology. This scale turns out to be l(UV) similar or equal to 5 l(P) for Lambda(OBS) similar or equal to 0 and we therefore argue that the smallness of Lambda(OBS) guarantees that Lorentz invariance is broken only at very small scales. We are also able to provide a first rough estimation for the values of the parameters of the theory mu and Lambda(W)