Variation of the speed of light and a minimum speed in the scenario of an inflationary universe with accelerated expansion

TL;DR

This paper explores how the speed of light and a minimum speed vary with the universe's temperature in an inflationary scenario, proposing a deformed relativistic framework consistent with special relativity.

Contribution

It introduces a deformed relativistic dynamics called Symmetrical Special Relativity that links the speed of light and minimum speed to the universe's temperature without violating SR.

Findings

Speed of light varies with cosmic temperature, being higher in the early universe.

The minimum speed also depends on the background temperature.

Varying speed of light theories may not solve the horizon problem.

Abstract

In this paper we aim to investigate a deformed relativistic dynamics well-known as Symmetrical Special Relativity (SSR) related to a cosmic background field that plays the role of a variable vacuum energy density associated to the temperature of the expanding universe with a cosmic inflation in its early time and an accelerated expansion for its very far future time. In this scenario, we show that the speed of light and an invariant minimum speed present an explicit dependence on the background temperature of the expanding universe. Although finding the speed of light in the early universe with very high temperature and also in the very old one with very low temperature, being respectively much larger and much smaller than its current value, our approach does not violate the postulate of Special Relativity (SR), which claims the speed of light is invariant in a kinematics point of view. Moreover, it is shown that the high value of the speed of light in the early universe was drastically decreased and increased respectively before the beginning of the inflationary period. So we are led to conclude that the theory of Varying Speed of Light (VSL) should be questioned as a possible solution of the horizon problem for the hot universe.