Determine the asymptotic large-boost gravitational-wave spectrum

Determine the asymptotic large-boost limit of the normalized gravitational-wave spectrum, including whether the peak amplitude and spectral shape approach boost-independent values at collision boosts much larger than the characteristic boosts studied.

Background

The paper uses the pairwise surrogate to study vacuum phase transitions at characteristic collision boosts up to γ∗=16\gamma_*=16, beyond the practical reach of direct many-bubble lattice simulations. The normalized peak amplitude decreases with increasing boost, but this decrease becomes small over the range 10≤γ∗≤1610\leq\gamma_*\leq16, while the post-peak spectral shape remains dependent on the scalar potential.

The observed trend suggests that simulations at characteristic boosts of order ten may already approximate the peak amplitude at much larger boosts, but the available calculations do not establish the limiting behavior. Determining the asymptotic regime would clarify whether the observed near-saturation persists and whether potential-dependent spectral-shape differences survive at arbitrarily large collision boosts.

References

If this trend continues, spectra computed at $\gamma_*\sim\mathcal O(10)$ already capture the peak amplitude of transitions with much larger boosts, although our results do not establish the asymptotic limit.

— A Pairwise Surrogate for Gravitational-Wave Spectra from Highly Relativistic Vacuum Bubble Collisions  (2610.12389 - Buschmann et al., 8 Oct 2026) in Section 7, Discussion and conclusions (following Section 7.1, Dependence on characteristic boost)