Some Impacts of Lorentz Violation on Cosmology

TL;DR

This paper explores how Lorentz violation influences scalar field dynamics in cosmology, deriving exact solutions and analyzing inflationary scenarios within a scalar-vector-tensor framework, highlighting effects on the universe's expansion and stability.

Contribution

It introduces a generalized dynamical equation for Lorentz-violating scalar-vector-tensor gravity and analyzes exact solutions and inflationary dynamics with various potentials.

Findings

Constant equation of state in de Sitter space

Power law expansion with quadratic coupling vector

Dynamic equation of state for n>2

Abstract

The impact of Lorentz violation on the dynamics of a scalar field is investigated. In particular, we study the dynamics of a scalar field in the scalar-vector-tensor theory where the vector field is constrained to be unity and time like. By taking a generic form of the scalar field action, a generalized dynamical equation for the scalar-vector-tensor theory of gravity is obtained to describe the cosmological solutions. We present a class of exact solutions for an ordinary scalar field or phantom field corresponding to a power law coupling vector and the Hubble parameter. As the results, we find a constant equation of state in de Sitter space-time and power law expansion with the quadratic of coupling vector, while a dynamic equation of state is obtained for $n> 2$. Then, we consider the inflationary scenario based on the Lorentz violating scalar-vector-tensor theory of gravity with general power-law coupling vector and two typical potentials: inverse power-law and power-law potentials. In fact, both the coupling vector and the potential models affect the dynamics of the inflationary solutions. Finally, we use the dynamical system formalism to study the attractor behavior of a cosmological model containing a scalar field endowed with a quadratic coupling vector and a chaotic potential.