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It is well-known that allowing for spatial curvature affects constraints oncosmological parameters such as the dark energy equation of state parameters.Here we study the effect of curvature on constraints on parameters used to testgeneral relativity (GR) at cosmological scales, commonly known as modifiedgrowth (MG) parameters, as while current data taken in the context of the$\Lambda$CDM model points to a universe that is flat or very close to it, thisconstraint may not hold in modified theories of gravity. Using the latestcosmological data sets we find that MG parameters are correlated with thecurvature parameter $\Omega_k$ and the constraints on the MG parameters areweakened compared to when $\Omega_k$ is not included in the parameter analysis.We next use various future simulated data sets, including cosmic microwavebackground, weak lensing, and Integrated Sachs-Wolfe-galaxy cross-correlations,where the fiducial model is spatially curved but we assume a flat model whenfitting the MG parameters. We find the assumption of a spatially flat model ona spatially curved universe does indeed cause an artificial shift in theconstraints on the MG parameters, in some cases even producing an apparentdeviation from GR in the MG parameter space. For our simulated data, tensionwith GR begins to manifest itself for fiducial models with $\abs{\Omega_k} \geq0.02$ and apparent deviations appear for $\abs{\Omega_k} \geq 0.05$. We findthat for negatively curved models the apparent deviation is more significant.The manifestation of this apparent deviation from GR due to the assumption ofspatial flatness above leads one to conclude that, when using futurehigh-precision data to perform these tests, spatial curvature must be includedin the parameter analysis along with the other core cosmological parameters andthe MG parameters.

Spatial curvature and cosmological tests of general relativity