Time evolution of thermodynamic temperature in the early stage of universe
F. Márkus [1], F. Vázquez [2], K. Gambár [3]

[1] Department of Physics, Budapest University of Technology and Economics, Budafoki 8, H-1521 Budapest, Hungary, [2] Department of Physics, Universidad Autonoma de Morelos, Cuernavaca, Mor., Mexico, [3] Dennis Gabor Applied University, Etele ut 68, H-1115 Budapest Hungary

Abstract: We show a possible way to introduce naturally the concept of a Lorentz invariant dynamical temperature which may be a thermodynamic parameter in cosmological models. This is done within the framework of classical field theory. A scalar field $\varphi$ is introduced which acts as a potential function to generate the (thermo)dynamic temperature. Such a potential allows us to describe the time evolution of this fundamental thermal property in the framework of inflationary models of the early universe. The dynamics contains a phase transition dividing the energy propagation into a dissipative and a non-dissipative process involving a spontaneous symmetry breaking mechanism. We find that the time evolution of the inflation field $\phi$ involves two main stages: first it decreases in the inflation period and later, after a long time, it starts to oscillate with a decreasing amplitude. It is shown that the general behavior of the thermal field $\varphi$ differs from that of the inflation field. It decreases reaching its minimal value and then, at about the beginning of the oscillating stage, it increases monotonically converting the energy of the inflation field into heat in the post-inflationary reheating process. This description is in line with cosmological inflationary models.