Large scale evolution of the curvature perturbation in Horava-Lifshitz cosmology

TL;DR

This paper investigates how the curvature perturbation evolves on large scales in Horava-Lifshitz cosmology, highlighting the role of an extra dark-matter-like component arising from the theory's unique constraints.

Contribution

It analyzes the large-scale evolution of curvature perturbations in Horava-Lifshitz gravity, accounting for the additional dark-matter-like component and clarifying conditions for conservation.

Findings

Curvature perturbation evolution is affected by the extra component.

Conditions for conservation depend on specific evolution equations.

Large-scale behavior differs from standard cosmology.

Abstract

In the non-relativistic theory of gravity recently proposed by Horava, the Hamiltonian constraint is not satisfied locally at each point in space. The absence of the local Hamiltonian constraint allows the system to have an extra dark-matter-like component as an integration constant. We discuss consequences of this fact in the context of cosmological perturbations, paying a particular attention to the large scale evolution of the curvature perturbation. The curvature perturbation is defined in a gauge invariant manner with this ``dark matter'' taken into account. We then clarify the conditions under which the curvature perturbation is conserved on large scales. This is done by using the evolution equations.