Beyond the classical distance-redshift test: cross-correlating redshift-free standard candles and sirens with redshift surveys

LSST will supply up to ${10}^6$ supernovae (SNe) to constrain dark energy through the distance-redshift ($D_L$-$z$) test. Obtaining spectroscopic SN redshifts (spec-$z$s) is unfeasible; alternatives are suboptimal and may be biased. We propose a powerful multi-tracer generalization of the Alcock-Paczynski test that pairs redshift-free distance tracers and an overlapping galaxy redshift survey. Cross-correlating $5\times {10}^4$ redshift-free SNe with DESI or Euclid outperforms the classical $D_L$-$z$ test with spec-$z$s for all SN. Our method also applies to gravitational wave sirens or any redshift-free distance tracer.