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

Abstract

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 ($k_{\max }\simeq 0.15h{\mathrm{Mpc}}^{-1}$), we find that our estimator is competitive with the more exhaustive direct bispectrum approach. This shows that surveys like DESI can already benefit from the quadratic estimator approach.

Published in the Open Journal of Astrophysics. 37 pages, 20 figures

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