Matter bounce in Hořava-Lifshitz cosmology

Hořava-Lifshitz gravity, a recent proposal for a UV-complete renormalizable gravity theory, may lead to a bouncing cosmology. In this article we argue that Hořava-Lifshitz cosmology may yield a concrete realization of the matter bounce scenario and thus give rise to an alternative to inflation for producing a scale-invariant spectrum of cosmological perturbations. In this scenario, quantum vacuum fluctuations exit the Hubble radius in the prebounce phase, and the spectrum is transformed into a scale-invariant one on super-Hubble scales before the bounce because the long wavelength modes undergo squeezing of their wave functions for a longer period of time than shorter wavelength modes. The scale invariance of the spectrum of curvature fluctuations is preserved during and after the bounce. A distinctive prediction of this scenario is the amplitude and shape of the bispectrum.

Figure 1

A space-time sketch of the matter bounce scenario. The vertical axis is time, with $t=0$ being the bounce time. The horizontal axis denotes comoving distance. The curve with the label $H$ is the Hubble radius $H^{-1}$; in comoving coordinates, the vertical line labeled by $k$ denotes the comoving wavelength of a fluctuation mode. This mode crosses the Hubble radius in the contracting phase before the time $-t_c$, when the period of matter domination ends.