jill-f-rankin

Introduces an effective spectral participation density dN_eff/dω = N_b(r,ω,t)·P_occ(ω,φ_q)·g(ω) that captures how time-dependent boundaries dynamically reorganize the local field-mode spectrum and thereby modify interaction rates without changing fundamental field theory. The framework is validated with perturbation theory, Floquet analysis, and 1-D FDTD simulations and yields testable predictions—mode broadening, sidebands, and transport/emission corrections—relevant to plasmas, cavity QED, and engineered photonic media.

A first-order cosmological phase transition generates gravitational waves through bubble collisions, sound waves, and turbulence. Standard calculations predict a smooth spectrum. This paper asks: what if the anisotropic stress tensor of the source has discrete scale invariance — a self-similar structure at discrete scaling ratios? The answer is that the DSI imprints a multiplicative log-periodic modulation directly onto the observable spectrum: Ω_GW(f) = Ω⁰_GW(f) · [1 + ε cos(2π ln(f/f*) / ln b)]. The key technical result is a factorization theorem — in the short-correlation-time limit (valid when β/H ≳ 10, which covers essentially all realistic phase transitions), the DSI modulation in the source transfers cleanly and multiplicatively to the gravitational wave spectrum, with corrections suppressed at the percent level. As a concrete UV completion, the paper embeds the DSI in walking technicolor, a real beyond-Standard-Model gauge theory already known to produce LISA-detectable gravitational waves. The WTC parameter space predicts ε ∈ [0.04, 0.18] and b ∈ [1.7, 2.8] — which lands precisely in the high-SNR corner of the LISA detectability plane. The log-periodic signature is therefore not a mathematical curiosity but a sharp, falsifiable prediction: if walking technicolor is the correct hidden sector, LISA should see ripples on the gravitational wave background at ratios b^n in frequency space.