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Primordial Black Holes in the Aldred Frame: A Formation Floor, a Truncated Spectrum, and the Remnant Abundance Ceiling

Year: 2026
Type: preprint
Abstract: Applies the Aldred frame (Einstein-Cartan spin-torsion gravity with density cap rho_A = 9.72e54 g/cm^3; collapse floor and evaporation remnant coincident at 8.66e13 g for a uniform core) to primordial black hole formation in the radiation era. (a) Standard spectrum: with M_H = c^3 t/G, a stated piecewise-constant g*(T) treatment, and gamma = 0.2, formation opens at 4.35e-6 g at the Planck time and reaches 8.07e37 g by t = 1 s. (b) The frame's modification: no primordial black hole can form below the floor mass 8.66e13 g, removing 19.3 orders of magnitude from the low-mass end and closing formation before t = 1.07e-24 s (T = 4.67e11 MeV); formation efficiency above the floor is unchanged, the torsion correction at horizon entry being (M_floor/M_H)^2 = 4.0% at the floor and 3.0e-4 at 1e15 g, so only the floor is new. (c) Abundance ceiling: every hole born in the evaporating window 8.66e13 g to 5.14e14 g leaves a non-evaporating 8.66e13 g remnant with present density Omega_rem,0 = beta (M_rem/M) Omega_r,0 (1+z_form); requiring remnants not to exceed the dark-matter density gives beta <= 4.83e-19 at the floor, 6.00e-19 at 1e14 g, and 6.99e-18 at 5.14e14 g. Scenarios in the window above the ceiling overclose the universe in this frame and are excluded (at 1e14 g, beta = 1e-15 gives Omega_rem,0 = 442, versus 1.1e-16 for the same scenario with Planck-mass remnants); scenarios at or below the published evaporation ceilings survive, and remnants as all of the dark matter (beta = beta_max) imply n_0 = 2.61e-44 cm^-3, mean separation 22.5 AU. All numbers are produced by the deposited compute.py. AI-use disclosure: this paper was drafted and computed with the assistance of Dave, an AI assistant operated by Aldred Industries, under the direction of the author; all derivations, computations, and conclusions were reviewed against the frame's equations before deposit.
DOI: 10.5281/zenodo.24110741
Language: English
Open Access status: green
OpenAlex ID: W7225733667
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