Equilibrium matter fields in the early universe

We investigate the behaviour of matter and radiation in thermal equilibrium when there is a continuous mass spectrum of elementary particle states. The detailed forms of the density and pressure in the relativistic and non-relativistic limits are calculated for power-law and power-law times exponential forms for the density of states spectrum. The spectrum of fluctuations from thermal equilibrium is also derived in each case. These results are used to study the change in behaviour of Friedman universes when there exists a continuous spectrum of mass states in the early universe. The results are compared with the standard picture which assumes a discrete spectrum of elementary particle mass states. Connections with string theories are also discussed. (author)