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

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.

arXiv comment21 pages, 4 figures

References in corpus (24)

• Cool horizons for entangled black holes
• Accelerated expansion of the universe driven by tachyonic matter
• Cosmological Evolution of the Rolling Tachyon
• Eternal inflation and its implications
• de Sitter special relativity
• A Machian Model of Dark Energy
• Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory
• Inflation in a closed universe
• Nordstrom's scalar theory of gravity and the equivalence principle
• Deformed Special Relativity with an energy barrier of a minimum speed
• Doubly Special Relativity with a minimum speed and the search for a quantum gravity at low energies
• A Singular Conformal Spacetime
• AdS and dS black hole solutions in analogue gravity: The relativistic and non-relativistic cases
• Doubly Special Relativity with a minimum speed and the Uncertainty Principle
• An explanation for the tiny value of the cosmological constant and the low vacuum energy density
• Deformed special relativity with an invariant minimum speed and its cosmological implications
• On FRW Model in Conformal Teleparallel Gravity
• Testing Lorentz symmetry violation with an invariant minimum speed
• On Dark Energy and Accelerated Reference Frames
• Gauge Theories on de Sitter space and Killing Vectors
• Lorentz violation with a universal minimum speed as foundation of de Sitter relativity
• On Gravitational Entropy of de Sitter Universe
• On the electrodynamics of moving particles in a quasi flat spacetime with Lorentz violation and its cosmological implications
• de Sitter-invariant special relativity and the dark energy problem

Cited by in corpus (7)

• An alternative to dark matter and dark energy: Scale-dependent gravity in superfluid vacuum theory
• Deformed Special Relativity with an invariant minimum speed as an explanation of the cosmological constant
• Lorentz violation with an invariant minimum speed as foundation of the uncertainty principle in Minkowski, dS and AdS spaces
• A brief review of a modified relativity that explains cosmological constant
• The importance of scalar fields as extradimensional metric components in Kaluza-Klein models
• The K-essence flow seen from the preferred frame $S_V$. A scalar field theory with Landau superfluid structure
• Cosmology of the Symmetrical Relativity versus Spontaneous Creation of the Universe Ex Nihilo