In this paper, the issue of how to introduce matter in Hoava-Lifshitz theories of gravity is addressed. This is a key point in order to complete the proper definition of these theories and, more importantly, to study their possible phenomenological implications. As is well known, in Hoava-Lifshitz gravity, the breakdown of Lorentz invariance invalidates the usual notion of minimally coupled matter. Two different approaches to bypass this problem are described here. One is based on a Kaluza-Klein reinterpretation of the 3+1 decomposition of the gravity degrees of freedom, which naturally leads to a definition of a U(1) gauge symmetry and, hence, to a new type of minimal coupling. The other approach relies on a midi-superspace formalism and the subsequent parametrization of the matter stress-energy tensor in terms of deep infrared variables. Using the last option, the phase space of Hoava-Lifshitz cosmology in the presence of general matter couplings is studied. It is found, in particular, that the equation of state of the effective matter may be very different from the actual matter one, owing to the nonlinear interactions which exist between matter and gravity. © 2011 IOP Publishing Ltd.
Carloni, S., Elizalde, E., & Silva, P. J. (2011). Matter couplings in Hoava-Lifshitz theories and their cosmological applications. Classical and Quantum Gravity, 28(19), . https://doi.org/10.1088/0264-9381/28/19/195002