Density reconstruction from biased tracers: Testing the equivalence principle through consistency relations

Consistency relations of large-scale structure offer a unique and powerful test of the weak equivalence principle (EP) on cosmological scales. If the EP is violated, different tracers will undergo different accelerations in response to a uniform gravitational field, and this loss of universality manifests as a dipole with a characteristic $1/K$ scale dependence in the squeezed limit of the bispectrum. In this work we show that such a violation can be identified with a particular anti-symmetric {modulation} in the local cross-power spectrum of distinct tracers. Based on this observation, we propose to test the EP using quadratic estimators as a more practical alternative to the conventional approach of directly estimating the bispectrum. We apply our quadratic estimator to a DESI-like survey and forecast constraints on the overall amplitude of EP violation. Including mildly nonlinear scales in our reconstruction ($k_\mathrm{max}\simeq0.15\, h\,\mathrm{Mpc}^{-1}$), we find that our estimator is competitive with the more exhaustive direct bispectrum approach. This means surveys like DESI can already benefit from the quadratic estimator approach.