Testing a minimal one-parameter background extension with DESI DR1 BAO data and standard sirens

The Hubble tension becomes particularly acute when Baryon Acoustic Oscillation (BAO) data are forced to accommodate a local Hubble-constant prior. Rather than proposing a full alternative cosmology, we investigate whether a minimal one-parameter extension of the background expansion can absorb this mismatch. The modification introduces a single effective density term, ₑ₇₄₎, to the Friedmann equation, interpreted phenomenologically as a delayed or non-instantaneous macroscopic background response. Under a strict local prior of H₀ = 73. 0\, km\, s^-1\, Mpc^{-1}, this extension reduces the full-covariance ² against 12 recent DESI DR1 BAO measurements from 209. 1 (for a standard CDM baseline) to 22. 4. While this represents a conditional consistency test rather than a global preference over CDM, the framework distinguishes itself by yielding a falsifiable multi-messenger prediction: a redshift-dependent offset, dL/dL (1+z), between electromagnetic and gravitational-wave luminosity distances. This effect remains negligible for local events such as GW170817, but reaches the sub-percent to percent level at cosmological redshifts, offering a direct observational discriminant for future standard-siren surveys.