Can particle production rescue Einstein-Cartan bounces from shear? A constraint on the production rate

In Bianchi I Einstein-Cartan (EC) cosmology with an unpolarized Weyssenhoff spin fluid, the torsion repulsion ∝ a⁻⁶ and the kinematic shear σ² ∝ a⁻⁶ enter the Friedmann constraint with identical exponents and opposite signs. Their ratio, the race parameter W ≡ 8πGαn_f²/(c²σ²), is therefore a constant of the motion: the bounce-versus-singularity verdict is fixed by initial data. A bounce requires σ/H < 4.2×10⁻²¹ at nuclear density; generic stellar collapse delivers σ/H ~ 3×10⁻⁵–3, failing by 32–42 orders of magnitude in W. The proposed rescue [Popławski, GRG 53, 18 (2021)] is gravitational particle production with ansatz (1/√−g) d(√−g n_f)/dt = βH⁴, with β a free parameter and the bounce conditional on "particle production dominating over shear." We pin β with three independent constraints: (i) a dimensional argument — QFT in curved spacetime contains ℏ, c, and the local curvature scale but no G, forcing β = f/c³ with f ~ O(g*) — confirmed by an explicit Bogoliubov computation on the Kasner collapse background giving f ≈ 0.05 per massless Dirac species, with the σ⁵ scaling exact; (ii) a back-reaction ledger — the fractional shear drained per e-fold is Δ = 8πf(σt_P)², about 10⁻⁷⁶ at nuclear density (for f ~ g* ~ 10²) and reaching O(1) only within the final e-fold of the 31-e-fold plunge to the Planck boundary; (iii) a collapse-energetics bound — the f ~ 10⁷⁸ required for a sub-Planckian rescue would inject ~10⁴⁷ J per quarter-millisecond into every collapsing stellar core from the vacuum — exceeding even the total neutrino budget (~10⁴⁶ J) of a core-collapse supernova by an order of magnitude — which observed core collapse excludes. The drain ledger is confirmed on the exact Kantowski-Sachs background by numerically integrating Popławski's own field equations. The conclusion is a constraint, not a model choice: particle production cannot dominate shear anywhere below the Planck boundary.