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The combination of multiple cosmological probes can produce measurements ofcosmological parameters much more stringent than those possible with anyindividual probe. We examine the combination of two highly correlated probes oflate-time structure growth: (i) weak gravitational lensing from a survey withphotometric redshifts and (ii) galaxy clustering and redshift space distortionsfrom a survey with spectroscopic redshifts. We choose generic survey designs sothat our results are applicable to a range of current and future photometricredshift (e.g. KiDS, DES, HSC, Euclid) and spectroscopic redshift (e.g. DESI,4MOST, Sumire) surveys. Combining the surveys greatly improves their power tomeasure both dark energy and modified gravity. An independent, non-overlappingcombination sees a dark energy figure of merit more than 4 times larger thanthat produced by either survey alone. The powerful synergies between thesurveys are strongest for modified gravity, where their constraints areorthogonal, producing a non-overlapping joint figure of merit nearly 2 ordersof magnitude larger than either alone. Our projected angular power spectrumformalism makes it easy to model the cross-correlation observable when thesurveys overlap on the sky, producing a joint data vector and full covariancematrix. We calculate a same-sky improvement factor, from the inclusion of thesecross-correlations, relative to non-overlapping surveys. We find nearly afactor of 4 for dark energy and more than a factor of 2 for modified gravity.The exact forecast figures of merit and same-sky benefits can be radicallyaffected by a range of forecasts assumption, which we explore methodically in asensitivity analysis. We show that that our fiducial assumptions produce robustresults which give a good average picture of the science return from combiningphotometric and spectroscopic surveys.

Optimising Spectroscopic and Photometric Galaxy Surveys: Same-sky Benefits for Dark Energy and Modified Gravity