<i>Euclid</i> : Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes

We forecast the constraints that the Euclid mission will place on the Hu–Sawicki f ( R ) modified gravity model using galaxy clustering and weak lensing observations. Euclid ’s primary probes will provide spectroscopic redshifts, photometric angular clustering, and weak lensing cosmic shear, thus allowing for precise tests of deviations from general relativity. We consider these observables to evaluate how well Euclid can constrain the extended model parameter f R 0 . For a fiducial value of | f R 0 | = 5 × 10 −6 , we find that in our baseline pessimistic setting, Euclid will constrain log 10 | f R 0 | at the 4% level with spectroscopic clustering, at 2.7% with the cross-correlation of photometric probes, and at 1.8% when combining all primary probes. This corresponds to an estimation on this model parameter of approximately | f R 0 = (5.0 +1.2 −0.9 × 10 −6 at the 1 σ level. We also forecast constraints for models with | f R 0 | = 5 × 10 −5 and | f R 0 | = 5 × 10 −7 , finding that Euclid will distinguish these from the standard cosmological model at more than 3 σ when using the full combination of primary probes. Euclid will be a powerful experiment to test modifications to gravity, provided that the theoretical systematics of the non-linear modelling are kept under control.