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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi>/</mml:mi> <mml:mi>K</mml:mi> </mml:mrow> </mml:math> 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">x</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≃</mml:mo> <mml:mn>0.15</mml:mn> <mml:mspace width="0.167em"/> <mml:mi>h</mml:mi> <mml:mspace width="0.167em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ), 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.