Lorentz violation with an invariant minimum speed as foundation of the tachyonic inflation within a Machian scenario
arXiv:2011.09844 · doi:10.1016/j.dark.2018.09.003
Abstract
We show the relationship between the scalar kinematics potential of Symmetrical Special Relativity (SSR) and the ultra-referential of vacuum connected to an invariant minimum speed postulated by SSR. The property of the conformal metric of SSR is showed, from where we deduce a kind of de Sitter metric. The negative curvature of spacetime is calculated from the conformal property of the metric. Einstein equation provides an energy-momentum tensor which is proportional to SSR-metric. We also realize that SSR leads to a deformed kinematics with quantum aspects directly related to the delocalization of the particle and thus being connected to the uncertainty principle. We finish this work by identifying the lagrangian of SSR with the so-called tachyonic models (slow-roll), where the tachyonic potential is a function depending on the conformal factor, thus allowing the SSR-lagrangian to be able to mimic a tachyonic lagrangian related to the so-called Dirac-Born-Infeld lagrangian, where the superluminal effects are interpreted as being a large stretching of spacetime due to new relativistic effects close to the invariant minimum speed as being the foundation of the inflationary vacuum connected to a variable cosmological parameter that recovers the cosmological constant for the current universe.
21 pages, 4 figures
References in corpus (7)
- Eternal inflation and its implications
- de Sitter special relativity
- Inflation in a closed universe
- Doubly Special Relativity with a minimum speed and the search for a quantum gravity at low energies
- AdS and dS black hole solutions in analogue gravity: The relativistic and non-relativistic cases
- Gauge Theories on de Sitter space and Killing Vectors
- Lorentz violation with a universal minimum speed as foundation of de Sitter relativity