The Stochastic Background from a Universe of Bounces: The Summed Gravitational-Wave Background of Bounced-Core Mergers versus Singular Collapse

The stochastic gravitational-wave background from all compact-binary mergers in cosmic history is computed with the Phinney integral over 1e-9 to 1e3 Hz, using Planck-2018 cosmology, GWTC-3 merger rates and chirp masses, a Madau-Dickinson redshift evolution, and Ajith et al. per-event spectra. The standard singular-collapse case gives Omega_GW(25 Hz) = 1.50e-9, a factor 2.26 below the LIGO/Virgo O3 upper limit and 1.33 below the O4a limit; in the pulsar-timing band the fiducial supermassive-binary background is Omega_GW = 3.12e-9 at 1/yr against 7.98e-9 for the NANOGrav 15-year process. The same integral is then computed in the Aldred frame (Einstein-Cartan spin-torsion gravity, rho_A = 9.72e54 g/cm^3), in which every merger remnant contains a bounced core, changing the per-event bookkeeping only through remnant retention (at most 4.8e-18 of one event's radiated energy), the torsion fraction at remnant densities (below 1e-39), echo redistribution (exactly zero in the frame's configuration), propagation (zero in vacuum), and the frame's fractional change to structure growth (envelope 9.9e-8). The frame and standard backgrounds differ by a relative amount no larger than 1.0e-7 at any frequency; the absolute frame shift at 25 Hz is 1.5e-16, about 3e-7 of the gap to the O4a limit and seven orders of magnitude below the merger-rate uncertainty. The negative result is stated at full size: the stochastic background cannot distinguish bounced cores from singular collapse, and cannot be the deciding factor in any detection claim. All numbers are produced by the deposited compute.py; the results are model calculations, not measurements. AI use is disclosed: this paper was drafted and computed with the assistance of Dave, an AI assistant operated by Aldred Industries, under the direction of the author. The author, William Alexander Aldred, directed the work and is sole author of record.