From photometric surveys to HI intensity mapping: Improving constraints on magnification biases while testing gravity

Combining photometric galaxy surveys with HI intensity mapping allows for high-precision measurements of magnification bias sG(z) and the gravity probe β. This multi-tracer approach breaks degeneracies between tracers, significantly improving constraints on $eta$ by factors of 25 to 50. The results enable testing general relativity on cosmological scales and constraining the sum of gravitational potentials $\Phi + \Psi$.

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