The Past-Hypothesis Cost of a Bounce: How Special the Pre-Bounce State Must Be

The required phase-space fraction is so small that its decimal logarithm is itself an astronomically large negative number. A bounce does not soften the past hypothesis; it relocates it. The contracting branch must arrive at the turnaround in a state every bit as atypical as the expanding branch is usually assumed to start in. The computation is performed from stated assumptions in a density-limited bounce, in which the neutron-branch limit density sets a maximum density, a finite bounce temperature, and a minimum horizon size. Headline values from the deposited calculation are: S_now_kB = 3.00e+89; S_max_kB = 2.90e+122; log10_phase_fraction = -1.26e+122; S_pre_max_kB = 3.00e+89; R_min_m = 1.29e-16; log10_N_horizon_volumes = 128. The study is simulated and computed, not measured, and its conclusions are stated at the precision the stated assumptions support.