General very special relativity in Finsler cosmology

Abstract

General Very Special Relativity (GVSR) is the curved space-time of Very Special Relativity (VSR) proposed by Cohen and Glashow. The geometry of GVSR possesses a line element of Finsler Geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified FRW cosmology for an osculating Riemannian space. The Friedman equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation

Born–Infeld electrodynamics in very special relativity

“…In a general form, we shall consider an action profile known as generalized Born-Infeld electrodynamics, in which we have an extended theory with two parameters [19]. Since we have already derived the wiggle field strength (9), we can define the following nonlinear Lagrangian density (13) where the invariants are defined as the following F = 1 4F μνF μν , and G = 1 4F μνG μν . As usual, the dual electromagnetic field strength tensor is given by G μν = 1 2 μνρλF ρλ .…”

“…Since our goal is to compute the electrostatic finite energy and the gauge-invariant scalar potential it suffices to our interest to consider only the invariant F term in the Lagrangian density (13).…”

Generalized relativistic dynamics in a non-inertial reference frame

“…(43a)-(44b) governing relativistic dynamics in non-inertial reference frames where both spacetime coordinates and corresponding velocities are variables, constitute the starting point for developing theoretical models for physics beyond Einstein's general relativity and the Standard Model in quantum field theory. Indeed, recent work by various authors [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] present models generally based on Finsler geometry (nonholonomic manifold) to account for the anisotropy of the gravitational field and Lorentz invariance violation effects. In particular, the models in [16][17][18][19][20][21][22][23][24] are to be understood as special or approximate versions of our field equations (43a)-(44b) in the sense that the field equations in those works are not based on the exact conservation laws, while at the same time some of them [17][18][19] are based on the Berwald covariant differentiation which is known to be nonmetric compatible [16,[20][21]23].…”

“…In particular, the models in [16][17][18][19][20][21][22][23][24] are to be understood as special or approximate versions of our field equations (43a)-(44b) in the sense that the field equations in those works are not based on the exact conservation laws, while at the same time some of them [17][18][19] are based on the Berwald covariant differentiation which is known to be nonmetric compatible [16,[20][21]23]. On the other hand, models in [14][15][25][26][27][28] attempt to account for the Lorentz invariance violation effects either within the Finsler geometric framework [14,15] or starting with the Cohen-Glashow model of Very Special Relativity [25] with its generalizations incorporating basic elements of Finsler geometry by other authors in [26][27][28].…”

Free Particle in Very Special Relativity, Gauge Symmetry and Two-Time Physics

“…Cohen and Glashow suggested that VSR might be important at Planck scale. It is worth to mention that Finsler geometry is a good framework for VSR [7] and a relation between this theory and non commutative spaces was found [8,9]. Furthermore, a generalized VSR was presented, where the usual line element is changed to [10] …”