The trans-planckian problem in the healthy extension of horava-lifshitz gravity

The Trans-Planckian Problem in the Healthy Extension of Horava-Lifshitz Gravity
Elisa G. M. Ferreira∗
Instituto de Instituto de F´ ısica, Universidade de S˜o Paulo, C.P. 66318, a 05315-970, S˜o Paulo, SP, Brazil and Department of Physics, a McGill University, Montr´al, QC, H3A 2T8, Canada e

Robert Brandenberger†
Department of Physics, McGill University, Montr´al, QC, H3A 2T8, Canada e (Dated: August 20, 2012) Planck scale physics may influence the evolution of cosmological fluctuations in the early stages of cosmological evolution. Because of the quasi-exponential redshifting, which occurs during an inflationary period, the physical wavelengths of comoving scales that correspond to the present large-scale structure of the Universe were smaller than the Planck length in the early stages of the inflationary period. This trans-Planckian effect was studied before using toy models. The HoravaLifshitz (HL) theory offers the chance to study this problem in a candidate UV complete theory of gravity. In this paper we study the evolution of cosmological perturbations according to HL gravity assuming that matter gives rise to an inflationary background. As is usually done in inflationary cosmology, we assume that the fluctuations originate in their minimum energy state. In the transPlanckian region the fluctuations obey a non-linear dispersion relation of Corley-Jacobson type. In the ”healthy extension” of HL gravity there is an extra degree of freedom which plays an important role in the UV region but decouples in the IR, and which influences the cosmological perturbations. We find that in spite of these important changes compared to the usual description, the overall scale-invariance of the power spectrum of cosmological perturbations is recovered. However, we obtain oscillations in the spectrum as a function of wavenumber with a relative amplitude of order unity and with an effective frequency which scales nonlinearly with wavenumber. Taking the usual inflationary parameters we