Lorentz violation with an invariant minimum speed as foundation of the tachyonic inflation within a Machian scenario

TL;DR

This paper explores how an invariant minimum speed in Symmetrical Special Relativity (SSR) can underpin tachyonic inflation, linking quantum aspects, spacetime geometry, and a variable cosmological constant within a Machian framework.

Contribution

It introduces a novel connection between SSR's invariant minimum speed and tachyonic inflation, deriving a de Sitter-like metric and a tachyonic Lagrangian from SSR principles.

Findings

Derivation of a de Sitter metric from SSR conformal properties

Identification of SSR Lagrangian with tachyonic models

Connection between SSR effects and a variable cosmological constant

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.