Renormalization procedure for the classical lattice computation of inflationary SIGWs

Develop a consistent procedure to properly renormalize the classical lattice computation of the inflationary second‑order gravitational‑wave spectrum and carefully derive the corresponding renormalized spectrum.

Background

The authors sketch the structure of the inflationary SIGW calculation and note that naive classical evaluations exhibit divergences, necessitating regularization and renormalization. In their preliminary implementation they set an arbitrary cutoff to obtain an order‑of‑magnitude estimate.

They explicitly state that both a careful derivation of the renormalized inflationary spectrum and a consistent renormalization procedure for the classical lattice output remain to be completed. Addressing this would clarify the physical inflationary contribution and enable robust comparisons with post‑reheating signals.

References

A careful derivation of the renormalized spectrum, as well as a consistent procedure to properly renormalize the (classical) lattice result, are left for future work, where we will consider scenarios in which this component is expected to dominate the total GW signal, such as the models analyzed in.

Lattice simulations of scalar-induced gravitational waves from inflation  (2604.03628 - Caravano et al., 4 Apr 2026) in Appendix A, Inflationary gravitational waves