The Spin-Temperature Coupling Epoch and Its Sensitivity to the Bounce

Before the first stars, the hydrogen spin temperature is tied to the gas by collisions; after they form, Lyman-alpha photons take over that role through the Wouthuysen-Field mechanism. Using the stated cosmology and the brightness-temperature relations described in the Methods, the calculation gives the following headline values: z couple = 22.5; z couple standard = 25; shift = -2.5; coupling x = 1.40. The comparison values taken from the published record — including the EDGES and SARAS reports, HERA limits and the Planck optical depth where relevant — are used exactly as published, and the bounce contribution enters only through the named timing, heating or shear inputs. The result is a computed prediction for the delayed-onset history, with its sensitivity to each input stated in the Discussion. This study is simulated and computed from stated assumptions; it is not a measurement.