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In this paper we aim to investigate a deformed relativistic dynamicswell-known as Symmetrical Special Relativity (SSR) related to a cosmicbackground field that plays the role of a variable vacuum energy densityassociated to the temperature of the expanding universe with a cosmic inflationin its early time and an accelerated expansion for its very far future time. Inthis scenario, we show that the speed of light and an invariant minimum speedpresent an explicit dependence on the background temperature of the expandinguniverse. Although finding the speed of light in the early universe with veryhigh temperature and also in the very old one with very low temperature, beingrespectively much larger and much smaller than its current value, our approachdoes not violate the postulate of Special Relativity (SR), which claims thespeed of light is invariant in a kinematics point of view. Moreover, it isshown that the high value of the speed of light in the early universe wasdrastically decreased and increased respectively before the beginning of theinflationary period. So we are led to conclude that the theory of Varying Speedof Light (VSL) should be questioned as a possible solution of the horizonproblem for the hot universe.

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