Bounce scenarios in the Sotiriou–Visser–Weinfurtner generalization of the projectable Horava–Lifshitz gravity

Abstract

Abstract.The occurrence of a bounce in the FRW cosmology requires modifications of General Relativity. An example of such a modification is the recently proposed Hořava-Lifshitz theory of gravity, which includes a "dark radiation" term with a negative coefficient in the analog of the Friedmann equation. A modification of the HL gravity, relaxing the "detailed balance" condition, brings additional terms to the equations of motion, corresponding to stiff matter. This paper presents comparison of the phase structure of the original and modified Hořava cosmology. Special attention is paid to the analysis of a wide range of bouncing solution, appearing in both versions of the Hořava theory.

Bianchi IX model: Reducing phase space

“…In what follows we try to understand local properties of the phase space of the system by using the method of nonlinear dynamical systems [18][19][20][21][22].…”

“…Apart from these, the compactification mapping is usually a noncanonical transformation that may lead to a Hamiltonian system that is different from the original one. The compactification is usually a very subtle procedure [6,21,22]. The set of finite and infinite critical points and their characteristics, given by the properties of the Jacobian matrix of the linearized equations at those points, may provide a qualitative description of a given dynamical system.…”

“…One may speculate that the infinities in (38) should be approached in such a way that x 3 ( x 2 ( x 1 . A much better way of dealing with the points at infinities would consist in an appropriate mapping of our phase space onto a compact region of R 6 by using, for instance, the Poincaré-type mapping [21,22]. Since in the present work we do not intend to analyze the set S B in terms of possible separatrices, we postpone making use of the compactification maps to our next paper.…”

Resolution of cosmological singularity in Hořava-Lifshitz cosmology

“…Significant work has been done on this theory examining and extending the properties of the theory [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Application of Hořava-Lifshitz gravity to a cosmological framework resulted in Hořava-Lifshitz cosmology, with a novel feature enabling the existence of bounce instead of initial singularity predicted by classical GR.…”

Hořava–Lifshitz cosmology in light of new data

“…It is also referred to as Hořava-Lifshitz (HL) gravity since if contains a fixed point in the UV with an anisotropic Lifshitz scaling between space and time, explicity breaking Lorentz invariance in the UV. A lot of work has gone into this model, including studies on cosmological solutions [20,21,22], dark radiation and braneworlds [22,23], and the resolution of the initial singularity [24,25,26]. Several papers have placed bounds on different regions of the Hořava-Lifshitz framework, for example using cosmological data [27], binary pulsars [28,29], and in the context of dark energy [30].…”