The Trans-Planckian Problem in the Healthy Extension of Horava-Lifshitz Gravity

TL;DR

This paper investigates how Planck-scale physics, modeled by Horava-Lifshitz gravity, affects the evolution of cosmological fluctuations during inflation, revealing oscillatory features in the power spectrum that are challenging to observe.

Contribution

It analyzes the trans-Planckian problem within the healthy extension of Horava-Lifshitz gravity, incorporating a non-linear dispersion relation and an extra degree of freedom.

Findings

Scale-invariance of the power spectrum is maintained.

Oscillations in the spectrum are introduced with large frequency.

Oscillation effects are likely unobservable due to high frequency.

Abstract

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 Horava-Lifshitz (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 trans-Planckian 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 find that the frequency of the oscillations is so large as to render the effect difficult to observe.