Determine the post-screening decay law for gravitational-wave sources

Determine the physical post-screening decay law governing scalar-gradient contributions to gravitational-wave production after a bubble wall covers part of another pair’s collision region, rather than relying on the phenomenological universal prescription \(K=\widehat D^{\,c}\) with \(c=3.6\).

Background

The pairwise surrogate accounts for the fact that scalar gradients can continue radiating after a collision region is covered by another bubble. It models this effect with a gradual screening prescription based on isolated-pair gradient relaxation, using a common phenomenological exponent $c=3.6$ calibrated against six many-bubble benchmarks.

The calibration improves agreement with lattice spectra, but the comparisons do not uniquely identify the correct decay law. A more physical treatment would need to determine how the additional wall interaction modifies the already-existing gradients, including possible dependence on collision boost, scalar potential, wall thickness, incidence angle, and the age of the collision region.