Gödel-type universes in bumblebee gravity

Abstract

The bumblebee field coupled with gravity is considered. This gravitational theory exhibits spontaneous breaking of Lorentz symmetry. The Gödel-type universe is introduced and then the causality and its violation are studied. Causal and non-causal Gödel-type solutions are obtained for different content of matter.In addition, when the coupling constant, which controls the interaction between the bumblebee field and the gravitational field, is zero the bumblebee potential may be associated with the value of the cosmological constant of the general relativity. Furthermore, the case with the non-zero coupling constant is also investigated.

Bumblebee field as a source of cosmological anisotropies

“…Then the geometry described by Eqs. ( 31)- (32) presents the planar symmetry in the x 2 − x 3 plane, and the anisotropic feature of that spacetime comes from δ. For δ ≪ 1, one has a small deviation from isotropy, and as the integration constants K 1 , K 2 , and K 3 are set to zero, the geometry given by Eqs.…”

“…That is, a universe described by Eqs. ( 31)- (32) emerges from the decoupling anisotropically and becomes isotropic as t → t 0 . Our interest here is from the decoupling to the present time, where we had a matter-dominated universe.…”

“…With the mean Hubble factor for a radiation plus matter universe, given by Eq. ( 49), we are able to find out the factor (33) and solve the directional Hubble parameters (31) and (32). By doing that, we have…”

Thermodynamics of massless particles in curved spacetime

“…Although the well-known theory of general relativity is certainly one of the most successful physical theories within theoretical and experimental viewpoints, there exist some alternative approaches to study gravity where the well-established Lorentz symmetry is no longer maintained [1][2][3][4][5]. Over the last years, many of them have received much attention, namely, Chern-Simons [6][7][8][9][10][11][12][13], Hȏrava-Lifshitz [14][15][16][17][18][19][20][21], Einstein-aether [22][23][24][25][26][27][28][29], Nieh-Yan [30], Bumblebee [31][32][33][34][35][36][37][38][39], and non-local [40][41][42][43][44][45] theories of gravity.…”

Schwarzschild Like Solution with Global Monopole in Bumblebee Gravity

“…On the other side, the Lorentz symmetry breaking is associated with the idea that the Quantum Gravity (QG) signals may emerge at low energy scales [4]. The naturelness and the possibility of Lorentz symmetry breaking is discussed in the context of string theory in [5][6][7][8][9][10][11][12][13][14][15]. The Lorentz symmety breaking arises in other theories like noncomutative field theories [16][17][18] and loop quantum gravity theory [19,20] among other scenarios [21][22][23][24].…”