Tunneling in cosmology and isothermal inflation

The wave function for the universe, as proposed by Hartle and Hawking, experiences tunneling for small values of the radius of the universe. This induces thermal effects and so a hot big bang. We first give a detailed analysis of the observer accelerating in Minkowski space in terms of the tunneling of his wave function beyond his turning point. Applied to cosmology one finds a temperature at the big bang equal to the Gibbons-Hawking value. The residual thermal effects which result in an isothermal inflationary expansion give rise to a renormalized self-consistently determined Hubble constant (and hence Gibbons-Hawking temperature) through the trace anomaly. A thermodynamic interpretation is given. These results militate against phase transitions as a motor for inflation. (orig.)