Novel geometrical test of cosmological expansion from photometric data

In tomographic cosmic-shear observations, the Bernardeau, Nishimichi, Taruya (BNT) transform allows us to build weak lensing transformed maps for which the contribution from low-redshift lenses is nulled. As this transformation depends specifically on the expansion rate of the Universe and is independent of the matter distribution properties, it can be leveraged to extract information from large-scale structure probes at arbitrary non-linear scales. Thus, it provides constraints on cosmological background evolution. We demonstrate the applicability of the BNT transform as a probe by designing a null test and evaluating its performance for Stage IV weak lensing projects. Using a Fisher matrix analysis combined with parameter sampling, we show that this approach can significantly enhance constraints on the dark energy equation of state. In such surveys, apart from photometric redshifts uncertainties, performance is expected to be limited primarily by shape noise, rather than cosmic variance, making substantial improvements possible thanks to better designed surveys in the future.