Renormalized analytical calculation of the inflationary SIGW contribution

Develop a consistent analytical treatment of the inflationary contribution to second‑order scalar‑induced gravitational waves by providing the renormalization needed to make the calculation well defined and comparable to the post‑reheating emission.

Background

In their setup, scalar-induced gravitational waves can be sourced both during inflation (near Hubble exit) and after reheating (at horizon re-entry), with the latter typically dominating in the scenarios studied. While the post‑reheating signal is handled with established semi‑analytical methods and lattice simulations, the authors note that the inflationary contribution requires special care due to divergences and the quantum nature of fluctuations near the horizon.

They include the inflationary contribution in their numerical pipeline for completeness but explicitly state that a fully consistent analytical prediction demands a renormalization procedure. Establishing such a renormalized framework would enable robust analytical comparisons to the numerically computed post‑reheating signal.