We show that, assuming the dispersion relation proposed recently by Horava in the context of quantum gravity, radiation energy density exhibits a peculiar dependence on the scale factor: the radiation energy density decreases proportional to a(-6). This simple scaling can have an impact on cosmology. As an example, we show that the resultant baryon asymmetry as well as the stochastic gravity waves can be enhanced. We also discuss current observational constraint on the dispersion relation. (C) 2009 Elsevier B.V. All rights reserved.