Quantum effects in the early universe. V. Finite particle production without trace anomalies

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 ξ=lρ_b/ρ_r^3/4, where l is the Planck length, ρ_b is the baryon energy density, and ρ_r is the radiation energy density, all in units where ℏ=c=1. For our universe ξ∼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 ξm_bl, where m_b is the mass of a typical baryon, and therefore very small.