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Horava gravity has been constructed so as to exhibit anisotropic scaling inthe ultraviolet, as this renders the theory power-counting renormalizable.However, when coupled to matter, the theory has been shown to suffer fromquadratic divergences. A way to cure these divergences is to add terms withboth time and space derivatives. We consider this extended version of thetheory in detail. We perform a perturbative analysis that includes all modes,determine the propagators and discuss how including mixed-derivative termsaffects them. We also consider the Lifshitz scalar with mixed-derivative termsas a toy model for power counting arguments and discuss the influence of suchterms on renormalizability.

Horava gravity with mixed derivative terms