The Planck Optical Depth Reproduced by a Bounce-Frame Reionisation History

The Thomson optical depth measured from cosmic microwave background polarisation is the most direct integral constraint on reionisation. Using the stated cosmology and the brightness-temperature relations described in the Methods, the calculation gives the following headline values: tau model = 0.058; tau planck = 0.054; tau planck err = 0.007; sigma diff = 0.6. 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.