Cosmological implications of the Gibbs ensemble in parametrized relativistic classical mechanics

Earlier investigators have shown that the free energy of an ideal gas in the ultrarelativistic (UR) regime of parametrized relativistic classical mechanics (PRCM) is different from the free energy calculated with use of the standard theory of relativistic classical mechanics (RCM). These differences do not become significant until very high temperatures are reached. Physical examples where the UR regime may be reached include the interior of stars, relativistic gas dynamics, and the first minute after the Big Bang. Of these, it is shown in the present paper that negligible differences are expected at realistic temperatures for relativistic gas dynamics and stellar models. This demonstration requires an evaluation of the PRCM and RCM free energies over a wide range of temperatures extending from the nonrelativistic limit to the UR limit. The greatest differences between PRCM and RCM are manifested in the density parameter of cosmological models. To study this effect, a general relativistic formalism is derived from variational principles within the context of PRCM. Scale factors and the age of Friedmann universes are calculated