HERA Power-Spectrum Limits and the Allowed Delay in Lyman-alpha Coupling

Interferometric limits from HERA on the 21-cm power spectrum at cosmic dawn already exclude the coldest, most strongly fluctuating scenarios in some redshift ranges. Using the stated cosmology and the brightness-temperature relations described in the Methods, the calculation gives the following headline values: z couple = 17.5; delay z = 2.5; power upper mK2 = 730; model power mK2 = 315. 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.