Matching second-order classical and 1-loop quantum tensor power spectra in de Sitter spacetime

Large corrections to the inflationary tensor power spectrum have been speculated to emerge either as second-order scalar-induced classical effects, or as 1-loop quantum corrections. These two sources are not independent of each other. Choosing the example of a massless minimally coupled scalar field, we show how the full 1-loop result can be divided into its classical and vacuum parts. Working first in dimensional regularization, we show that the classical part is IR divergent, with IR referring to small comoving momenta that have an influence for a very long time. In the full 1-loop quantum result, these divergences cancel. Introducing then a momentum cutoff that permits for a numerical evaluation of the classical contribution, we show that the IR sensitivity manifests itself as a cubic divergence. We suggest a procedure of "non-perturbative renormalization" for extracting physical information not affected by the divergence. If this can be implemented in realistic systems, it could consolidate numerical studies of inflationary scalar-induced gravitational waves.