  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.
