Cosmological gravity on all scales. Part IV. 3× 2 pt Fisher forecasts for pixelised phenomenological modified gravity

Stage-IV large scale structure surveys are promising probes of gravity on cosmological scales. Due to the vast model-space in the modified gravity literature, model-independent parameterisations represent useful and scalable ways to test extensions of ΛCDM. In this work we use a recently validated approach of computing the non-linear 3× 2 pt observables in modified gravity models with a time-varying effective gravitational constant μ and a gravitational slip η that is binned in redshift to produce Fisher forecasts for an LSST Y10-like survey. We also include in our modelling an effective nulling scheme for weak-lensing by applying the Bernardeau-Nishimichi-Taruya (BNT) transformation that localises the weak-lensing kernel enabling well-informed scale cuts. We show that the combination of improved non-linear modelling and better control of the scales that are modelled/cut yields high precision constraints on the cosmological and modified gravity parameters. We find that 4 redshift bins for μ of width corresponding to equal incremental ΛCDM growth is optimal given the state-of-the-art modelling and show how the BNT transformation can be used to mitigate the impact of small-scale systematic effects, such as baryonic feedback.