Model-independent test of prerecombination new physics: Measuring the sound horizon with gravitational wave standard sirens and the baryon acoustic oscillation angular scale

In a broad class of cosmological models where spacetime is described by a pseudo-Riemannian manifold, photons propagate along null geodesics, and their number is conserved, upcoming gravitational wave (GW) observations can be combined with measurements of the baryon acoustic oscillation (BAO) angular scale to provide model-independent estimates of the sound horizon at the baryon drag epoch. By focusing on the accuracy expected from forthcoming surveys such as the Laser Interferometer Space Antenna GW standard sirens and dark energy spectroscopic instrument (DESI) or Euclid angular BAO measurements, we forecast a relative precision of σ_{r_{d}}/r_{d}∼1.5% within the redshift range z≲1. This approach will offer a unique model-independent measure of a fundamental scale characterizing the early universe, which is competitive with model-dependent values inferred within specific theoretical frameworks. These measurements can serve as a consistency test for ΛCDM, potentially clarifying the nature of the Hubble tension and confirming or ruling out new physics prior to recombination with a statistical significance of ∼4σ.