Deformed special relativity with an invariant minimum speed and its cosmological implications

Abstract

It will be introduced a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest, by including a universal minimum limit of speed in the subatomic world. Such a lowest limit, unattainable by particles, represents a preferred reference frame associated with a universal background field that breaks Lorentz symmetry. Thus the structure of space-time is extended due to the presence of a vacuum energy density, which leads to a negative pressure at cosmological length scales. The tiny values of the cosmological constant and the vacuum energy density will be successfully obtained, being in good agreement with current observational results.

On the electrodynamics of moving particles in a quasi flat spacetime with Lorentz violation and its cosmological implications

“…(43). In summary, we have shown that there is a tiny dimensionless coupling constant (ξ = V /c ∼ 10 −22 ) that couples gravity with electromagnetic fields, where V (∼ 10 −14 m/s) is the universal minimum speed related to a preferred background frame (Section 5), which is associated to a uniform background field with low vacuum energy density connected to the cosmological "constant" Λ[11] [13]. This connection between Λ and V can already be obtained directly from Eq.…”

“…(43), where V ∝ √ G. The background field energy density ρ (2) em brings a new aspect of gravitation that needs to be thoroughly investigated. This new feature brings with it a change in our notion of space-time and, thus, also the concept of inertial frames (galilean frameworks) with regard to the motion of subatomic particles [11][12] [13]. This subject will be investigated in the next section.…”

“…In Section 4, we will obtain the value of the tiny dimensionless coupling constant ξ, where we find that ξ = V /c = Gm e m p /4πǫ 0 q e / c ∼ = 1.5302 × 10 −22 , V ( ∼ = 4.5876 × 10 −14 m/s) being interpreted as the universal minimum speed unattainable for any particle at lower energies, and of the same status as the speed of light c (maximum speed) for higher energies, in the sense that both speeds c and V are invariant. Thus, we have a new kind of DSR, that was denominated as Symmetrical Special Relativity (SSR) [11] [12] [13], where the unattainable minimum speed is associated with a privileged reference frame of background field (a non-luminiferous aether).…”

Lorentz violation with a universal minimum speed as foundation of de Sitter relativity

“…Now, we note that Lorentz symmetry breaking due to the presence of the ultrareferential S V connected to the dark energy that fills the sphere has origin in a nonclassical (nonlocal) aspect of gravity that leads to a repulsive gravitational potential (φ < 0). In order to see such an anti-gravity, let us consider the total energy of a proof particle on the surface of such a dark sphere according to SSR, [5][6][7] namely, from where we obtain…”

“…4 Symmetrical Special Relativity (SSR) is a theory that has recently appeared [5][6][7][8][9] as a new candidate for describing gravitational vacuum, from where it has already been possible to calculate the value of the cosmological constant and also discusses the origin of the uncertainty principle. 8 SSR is a kind of theory of deformed special relativity (DSR) with double limit of speeds, namely, a maximum limit of speed c (speed of light) and a minimum speed V .…”