Global dynamics of the Hořava–Lifshitz cosmological system

Abstract

Using the qualitative theory, the global dynamics of the cosmological model based on Hořava-Lifshitz gravity is described.

Global dynamics of Hořava–Lifshitz cosmology with non-zero curvature and a wide range of potentials

“…Our study will fully describes the global dynamics of system (7) in the region G = (x, z, s) ∈ R 3 : x 2 − z 2 ≤ 1 of physical interest adding its boundary at infinity. It should be noted from the derivation of system (7) that the space curvature k is implicit in the variables x and z.…”

“…In order to study the local phase portraits of the finite and infinite equilibrium points, and the global phase portraits of system (7) in the region G, which is the meaningful region for cosmology, see again [4] or [14]. We start discussing the phase portraits on its invariant planes and surface…”

“…In recent years Hořava [1] proposed a spacetime asymmetric gravitational theory similar to Lifshitz's scalar field theory, also known as Hořava-Lifshitz gravity. This theory has inspired a great deal of research for its applications in cosmology and black hole physics (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] or the review articles [19,20] and the references therein).…”

“…With or without detailed-balance condition, few researchers have published several papers on Hořava-Lifshitz gravity through phase space analysis, see for instance [3][4][5][6][7]17]. Among these papers there are also some of them about the case of non-zero space curvature k. When the terms related to k are dominant, Friedmann solution will be generated.…”

“…More precisely, they either studied the global dynamics of the planar case of Hořava-Lifshitz gravity with exponential potential by using the twodimensional Poincaré compactification, or discussed only local dynamics of this cosmological model with powerlaw potential but without investigate the dynamics close to infinity. The three-dimensional global dynamics of Hořavaa e-mail: gaofabao@sina.com (corresponding author) b e-mail: jllibre@mat.uab.cat Lifshitz cosmology with k = 0 and = 0 was studied in [7].…”