Scale-invariant cosmological perturbations from Horava-Lifshitz gravity without inflation

TL;DR

This paper addresses generating scale-invariant cosmological perturbations without inflation by leveraging Horava-Lifshitz gravity with dynamical exponent $z=3$. The UV dispersion $\omega^2 \propto k_{phy}^6$ causes quantum fluctuations of a free scalar field to freeze out independent of the Hubble rate, yielding a scale-invariant spectrum for suitable expansion histories (e.g., $a \propto t^p$ with $p>1/3$). The generated fluctuations are then converted into curvature perturbations via the curvaton mechanism or modulated decay of heavy fields, with the conversion possible in UV, IR, or intermediate epochs and before nucleosynthesis. The analysis shows a robust, non-inflationary pathway to the observed perturbation spectrum, without requiring the detailed balance condition, and predicts UV-driven scale invariance with potential mild tilt in intermediate regimes. Tensor perturbations are expected to share the UV-insensitive behavior, offering a consistent, testable alternative to inflationary scenarios.

Abstract

Based on the renormalizable theory of gravitation recently proposed by Horava, we present a simple scenario to generate almost scale-invariant, super-horizon curvature perturbations. The anisotropic scaling with dynamical critical exponent z=3 implies that the amplitude of quantum fluctuations of a free scalar field generated in the early epoch of the expanding universe is insensitive to the Hubble expansion rate and, thus, scale-invariant. Those fluctuations are later converted to curvature perturbations by the curvaton mechanism or/and the modulated decay of heavy particles/oscillating fields. This scenario works, for example, for power law expansion a\propto t^p with p>1/3 and, thus, does not require inflation. Also, this scenario does not rely on any additional assumptions such as the detailed balance condition.

Figures (1)

• Figure 1: Physical wavelength ($\sim a/k$) exits the sound horizon ($\sim (M^2H)^{-1/3}$) in the UV epoch ($H\gg M$) and re-enters the horizon ($\sim H^{-1}$) in the IR epoch ($H\ll M$). In this figure, a power-law expansion $a\propto t^p$ with $1/3<p<1$ is supposed.