Isotropic Cosmic Birefringence as a Rotation Rate: Degrees per Gigaparsec from Planck and Ground-Based Polarisation Measurements

This paper examines whether the reported uniform rotation of cosmic microwave background polarisation, expressed as a rate per unit distance, is large or small compared with the path over which it accumulates, and what that rate implies for any mechanism that builds the angle gradually along the line of sight. The calculation is performed from stated assumptions and published polarisation measurements, using the deposited script so that every quoted number can be reproduced. The headline outputs are: beta deg = 0.30; err deg = 0.11; deg per Gpc = 0.0216; err deg per Gpc = 0.0079; rad per m = 1.22e-29; significance = 2.7; second deg per Gpc = 0.0252. The treatment separates what the published measurements supply from what a theoretical framework must additionally provide; where a required quantity is not supplied, that absence is reported plainly as a negative result rather than replaced by an assumed value. The study is computed from stated assumptions and published inputs; it is not a new measurement. SIMULATED, NOT MEASURED in the sense that all derived quantities are calculated, not observed.