Cosmological Implication of the Trace Anomaly

We establish a connection between the trace anomaly and thermal radiation in the standard cosmology. This is done by solving the covariant conservation equation of the stress tensor associated with a conformally invariant quantum scalar field. The solution corresponds to thermal radiation with a temperature which is given in terms of a cut-off time excluding the spacetime regions very close to the initial singularity. We discuss the interrelation between this result and the result obtained in a two-dimensional Schwarzschild spacetime.