Abstract
We investigate primordial perturbations and non-gaussianities in the Hořava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Hořava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are " slow-roll suppressed” in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral-type non-gaussianity is of the order of unity, while the local-type non-gaussianity remains small, as in the usual single-field slow-roll inflation model in general relativity. Our result is a new constraint on Hořava-Lifshitz gravity.
Highlights
A renormalizable theory of gravity was proposed by Hořava [1,2,3]
Because of this anisotropic scaling, time plays a privileged role in the Hořava theory
The Hořava-Lifshitz theory allows a theory of gravitation that is scale-invariant in UV, while the standard general relativity (GR) with full diffeomorphism emerges at the IR fixed point
Summary
A renormalizable theory of gravity was proposed by Hořava [1,2,3]. This theory reduces to Einstein’s general relativity (GR) for large scales, and may be a candidate for the UV completion of general relativity. The Hořava-Lifshitz theory allows a theory of gravitation that is scale-invariant in UV, while the standard GR with full diffeomorphism emerges at the IR fixed point. In the UV limit, the scalar field perturbation is essentially scale-invariant and is insensitive to the expansion rate of the Universe, as has been addressed in [7,8,9,10]. We extend the previous works on cosmological perturbation theory in Hořava gravity, including nongaussianities. The basic idea is that, as has been addressed before, the divergence of the speed of light and the scale-invariance of the scalar perturbation in Hořava gravity indicate that there is no need to assume an exponential expansion of the Universe. We make a conclusion and discuss several related issues
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