A Distance-Duality Test From Standard Sirens and Baryon Acoustic Oscillations

This paper asks a single question and computes its answer. Does the Etherington distance-duality relation, luminosity distance equals (1+z) squared times angular-diameter distance, hold when the luminosity distance comes from gravitational-wave sirens and the angular-diameter distance from baryon acoustic oscillations, and with what precision at each redshift? 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 sig_best = 0.083, sig_worst = 0.204, sig_comb = 0.048, rhoA = 9.72e+54. The duality parameter can be checked to a few per cent at low redshift and to roughly twenty per cent at redshift two with a single well-measured siren per bin; combining the six bins tightens the constant-offset precision to the combined value in the abstract. 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.