I am reading this and honestly am thinking this is too simple, I can’t believe they overlooked this before.
It seems an obvious thing to test.
Maybe the problem was, group think prevented someone from presenting it because they were afraid of retribution from other scientists?
Link to the math: Solutions to Horava Gravity - H. Lu, Jianwei Mei, C.N. Pope
"........ Petr Horava introduced an intriguing idea - that one of the physical principles at the heart of general relativity might be violated. The principle is called Lorentz symmetry (or Lorentz invariance) and it is the principles that physics is the same in any reference frame. The Lorentz violation would only happen at very small scales, of course, which is why it's never been observed to be violated, but if Horava's theory is correct then a theory which doesn't include Lorentz invariance at small scales might still give rise to Lorentz invariance at large scales. The great benefit of this theory, if it can be fully worked out, is that it would be much easier to introduce quantum mechanics into the theory. (General relativity and quantum mechanics are not currently able to work together easily in the same theoretical frameworks.)
A team out of Texas A&M University have now investigated how Horava's theory would affect generic solutions of general relativity, such as those that are spherically symmetrical. Another physicist, Horatiu Nastase, has taken this work and believes that, as it currently exists, the scales are off and Lorentz invariance would only be replicated on scales larger than the observable universe. "Modifications of the detailed balance action, within Hořava theory, can cure this problem," explains Nastase. He also points out, "It is still not known if the quantum Hořava theory makes sense, and more work in that direction is needed."
Other alternative gravity theories, such as those discussed in John Moffat's Reinventing Gravity: A Physicist Goes Beyond Einstein, have been bouncing around in some form or another pretty much since before Einstein even completed general relativity in the first place. The difference between these other theories and the Horava theory, according to Nastase, is that "Hořava['s] theory presents the tantalizing possibility that we have a well-defined quantum theory at short distances, without the need for additional fields."