Complete analysis of linear cosmological perturbations in Hořava-Lifshitz gravity

Abstract

We investigate the linear cosmological perturbations in Hořava-Lifshitz gravity with a scalar field. Starting from the most general expressions of the metric perturbations as well as that of a canonical scalar field, we decompose the scalar, vector and tensor parts of the perturbed action.By reducing the Hamiltonian, we find that there are two independent degrees of freedom for the tensor perturbations while none for the vector perturbations. For the scalar perturbations, the remaining number of degrees of freedom, which are all gauge invariant, depends on whether the projectable condition is applied or not: two when applied, with one of them being possibly a ghost, and one when not applied. For both cases, we lose the time reparametrization symmetry of any kind.

On Gauge Invariant Cosmological Perturbations in UV-modified Hořava Gravity: A Brief Introduction

“…For example, tensor spectrum is scale invariant but scalar spectrum is not ! [3,4]. So, we need to break the detailed balancing in some way but without altering the improved UV behaviors of scale invariant tensor modes in the previous works [3,4] and we called it as "UV modifications" [5].…”

“…So in that case, the theory would not be renormalizable and nor scale invariant for scalar part, which is in contradict to observational data ! Now, in order to exhibit the true dynamical degrees of freedom we consider the Hamiltonian reduction method [10], for the cosmologically perturbed actions [4,11] and, after some computation, the action reduces to…”

“…al. [4], scalar spectrum are not scale-invariant though tensor spectrum does. This is today's topic and it provides a natural formulation of cosmology, known as "effective field theory (EFT)", by construction.…”

New symmetries in Fierz-Pauli massive gravity

“…Let us first consider the tensor modes, which do not have any associated constraint. Therefore, both tensor modes are physical degrees of freedom, and their Hamiltonian is exactly that of GR (see for example [18]). In the vector case, F i is the only dynamical degree, while S i appears as a Lagrange multiplier, enforcing the constraints Π i F = 0.…”

Oscillating universe in Hořava-Lifshitz gravity

“…Earlier works have indeed revealed some interesting aspects of HL cosmology such as dark matter as an integration constant [5], the generation of chiral gravitational waves from inflation [6], scale-invariant fluctuations without inflation [7], and a possible dark energy scenario [8][9][10]. There is also some discussion closely related to observational cosmology and astrophysics such as cosmological perturbation [7,[11][12][13][14][15][16][17][18][19][20][21][22], observational constraints [23][24][25], a primordial magnetic field without inflation [26], and a relativistic star [27,28].…”