[en] The production of scalar particles in a homogeneous isotropic spatially flat universe containing classical baryons and radiation is studied for regulated massless free-field theories without trace anomalies. The pair-production probability is evaluated to lowest nonvanishing order in the parameter j = lp/sub b//p/sub r//sup ts3/4/, where l is the Planck length, p/sub b/ is the baryon energy density, and p/sub r/ is the radiation energy density, all in units where h = c = 1. For our universe japprox.10^-27. The back reaction regulates the production of scalar particles near the singularity so that the probability to produce a pair in the volume occupied by one baryon over the history of the universe is finite, of order of magnitude jm/sub b/l, where m/sub b/ is the mass of a typical baryon, and therefore very small