Reheating After the Bounce: The Permitted Temperature Window, Expansion Bookkeeping, and Baryogenesis in the Aldred Frame

In Einstein-Cartan spin-torsion gravity, the universe in the Aldred frame contracts to the density limit rho_A = 9.72e54 g/cm^3 and re-expands. Companion computations bounded the density at which the observable primordial spectrum is laid down to rho_b <= 2.77e54 g/cm^3 (x_b <= 0.285 at 1 sigma) and showed that the frame's correction at big bang nucleosynthesis (BBN) densities is some fifty orders of magnitude below detectability. This paper prices the epoch between them: reheating, the thermalisation of the bounce's energy into the hot plasma. If a fraction eps_th of the exit energy density thermalises promptly, the reheating temperature is T_reh = eps_th^(1/4) T_max with T_max = 1.045e9 GeV for thermalisation at rho_A and 7.64e8 GeV at the Planck-compatible exit density rho_b. Against the robust BBN floor T_reh >= 4 MeV, the permitted window is open by 11.4 orders of magnitude, and any thermalisation efficiency above 2.16e-47 clears the BBN floor. A reheating epoch ending at 4 MeV contains N_re = 35.4 e-folds for equation of state w = 0 (30.3 for w = 1/6; 26.6 for w = 1/3) and shifts the pivot bookkeeping of the spectrum computation by Delta N_* = -8.85 e-folds in the w = 0 case, which would move an absolute slow-roll prediction of n_s by 0.0106, 2.5 times the Planck uncertainty; the spectrum computation's actual bound nevertheless survives, tightening only from x_b <= 0.285 to x_b <= 0.266. For baryogenesis, the exit must deliver eta = 6.12e-10 after reheating. Electroweak-scale and resonant leptogenesis operating windows fit inside the permitted window, but grand-unified baryogenesis at T ~ 1e16 GeV is excluded at any exit density the frame permits, and hierarchical thermal leptogenesis, which requires T_reh >= 1e9 GeV, is excluded at the Planck-compatible exit (required efficiency 2.94, greater than unity) and survives at the absolute ceiling only for eps_th >= 0.84. All numbers are produced by the deposited compute.py. AI use is disclosed: computational and drafting assistance was provided by Dave, an artificial intelligence system operated by Aldred Industries; the author, William Alexander Aldred, reviewed the computation and takes responsibility for the contents. The author is sole author of record.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-10
DOI
https://doi.org/10.5281/zenodo.24111238
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Reheating After the Bounce: The Permitted Temperature Window, Expansion Bookkeeping, and Baryogenesis in the Aldred Frame

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

Reheating After the Bounce: The Permitted Temperature Window, Expansion Bookkeeping, and Baryogenesis in the Aldred Frame

William Alexander Aldred
preprint en

Abstract

In Einstein-Cartan spin-torsion gravity, the universe in the Aldred frame contracts to the density limit rho_A = 9.72e54 g/cm^3 and re-expands. Companion computations bounded the density at which the observable primordial spectrum is laid down to rho_b <= 2.77e54 g/cm^3 (x_b <= 0.285 at 1 sigma) and showed that the frame's correction at big bang nucleosynthesis (BBN) densities is some fifty orders of magnitude below detectability. This paper prices the epoch between them: reheating, the thermalisation of the bounce's energy into the hot plasma. If a fraction eps_th of the exit energy density thermalises promptly, the reheating temperature is T_reh = eps_th^(1/4) T_max with T_max = 1.045e9 GeV for thermalisation at rho_A and 7.64e8 GeV at the Planck-compatible exit density rho_b. Against the robust BBN floor T_reh >= 4 MeV, the permitted window is open by 11.4 orders of magnitude, and any thermalisation efficiency above 2.16e-47 clears the BBN floor. A reheating epoch ending at 4 MeV contains N_re = 35.4 e-folds for equation of state w = 0 (30.3 for w = 1/6; 26.6 for w = 1/3) and shifts the pivot bookkeeping of the spectrum computation by Delta N_* = -8.85 e-folds in the w = 0 case, which would move an absolute slow-roll prediction of n_s by 0.0106, 2.5 times the Planck uncertainty; the spectrum computation's actual bound nevertheless survives, tightening only from x_b <= 0.285 to x_b <= 0.266. For baryogenesis, the exit must deliver eta = 6.12e-10 after reheating. Electroweak-scale and resonant leptogenesis operating windows fit inside the permitted window, but grand-unified baryogenesis at T ~ 1e16 GeV is excluded at any exit density the frame permits, and hierarchical thermal leptogenesis, which requires T_reh >= 1e9 GeV, is excluded at the Planck-compatible exit (required efficiency 2.94, greater than unity) and survives at the absolute ceiling only for eps_th >= 0.84. All numbers are produced by the deposited compute.py. AI use is disclosed: computational and drafting assistance was provided by Dave, an artificial intelligence system operated by Aldred Industries; the author, William Alexander Aldred, reviewed the computation and takes responsibility for the contents. The author is sole author of record.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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