Hořava-Lifshitz gravity with $\lambda \to \infty$

In the framework of the power-counting renormalizable theory of gravitation, recently proposed by Hořava, we study the limit $\lambda \to \infty$, which is arguably the most natural candidate for the ultraviolet fixed point of the renormalization group flow. In the projectable version with a dynamical critical exponent $z=3$, we analyze the Friedmann-Robertson-Walker background driven by the so-called “dark matter as integration constant” and perturbations around it. We show that amplitudes of quantum fluctuations for both scalar and tensor gravitons remain finite in the limit and that the theory is weakly coupled under a certain condition.