Modified Gravitational-Wave Propagation: The Friction Parameter and the Siren Distance Ratio

This paper asks a single question and computes its answer. If gravitational waves experience extra friction while travelling, their inferred luminosity distance differs from the electromagnetic one by a redshift-dependent ratio; what does that ratio look like for the standard two-parameter form, and which redshifts discriminate best between parameter values? Working in a flat LambdaCDM background and carrying the bounce-frame density ceiling explicitly — the Aldred Limit, rho_A = rho_Pl (m/m_Pl)^2/(8 pi C), with the neutron branch at 9.72e+54 g per cubic centimetre — the calculation gives the headline values r01 = 1.045, r1 = 1.250, r5 = 1.417, bestz = 5.0, rhoA = 9.72e+54. The ratio departs from unity slowly: even a large asymptotic deviation of fifty per cent appears as only a few per cent at redshift 0.1 and reaches its discriminating power beyond redshift one. Low-redshift bright sirens alone therefore cannot measure the friction parameter; the leverage is in distant sirens. Every number reported here comes from the deposited computation script, which states its assumptions in full. This study is simulated and computed from stated assumptions and published catalogue values; it is not a measurement.