  It is well-known that allowing for spatial curvature affects constraints on
cosmological parameters such as the dark energy equation of state parameters.
Here we study the effect of curvature on constraints on parameters used to test
general relativity (GR) at cosmological scales, commonly known as modified
growth (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, this
constraint may not hold in modified theories of gravity. Using the latest
cosmological data sets we find that MG parameters are correlated with the
curvature parameter $\Omega_k$ and the constraints on the MG parameters are
weakened compared to when $\Omega_k$ is not included in the parameter analysis.
We next use various future simulated data sets, including cosmic microwave
background, weak lensing, and Integrated Sachs-Wolfe-galaxy cross-correlations,
where the fiducial model is spatially curved but we assume a flat model when
fitting the MG parameters. We find the assumption of a spatially flat model on
a spatially curved universe does indeed cause an artificial shift in the
constraints on the MG parameters, in some cases even producing an apparent
deviation from GR in the MG parameter space. For our simulated data, tension
with GR begins to manifest itself for fiducial models with $\abs{\Omega_k} \geq
0.02$ and apparent deviations appear for $\abs{\Omega_k} \geq 0.05$. We find
that for negatively curved models the apparent deviation is more significant.
The manifestation of this apparent deviation from GR due to the assumption of
spatial flatness above leads one to conclude that, when using future
high-precision data to perform these tests, spatial curvature must be included
in the parameter analysis along with the other core cosmological parameters and
the MG parameters.
