The Post-Bounce Thermal History as a Source of Tilt Uncertainty: Reheating Temperature Bounds From the Spectral Index

The spectral index measured today depends, in a bounce cosmology, on the thermal history after the bounce, because that history decides how much expansion separates the bounce from the crossing of the pivot mode. This paper quantifies the dependence and inverts it into a bound on the reheating temperature. Shifting the post-bounce reheating temperature from 1e3 to 1e15 GeV moves the predicted index from 0.9575 to 0.9672, a spread of 0.009671, or 2.3 times the Planck uncertainty. Requiring the prediction to remain within two standard deviations of the Planck value excludes reheating temperatures below 50.4 GeV within this model, while no upper bound arises anywhere in the range studied, the scanned interval extending to 1e+15 GeV without leaving the band. The thermal history, often treated as a detail to be settled after the perturbation calculation, is therefore already constrained by the perturbation data themselves. A bounce model that specifies its spectrum but not its reheating has left a two-standard-deviation-sized hole in its prediction. The study is computed from stated assumptions, not measured.