  We investigate how pure-state Einstein-Podolsky-Rosen correlations in the
internal degrees of freedom of massive particles are affected by a curved
spacetime background described by extended theories of gravity. We consider
models for which the corrections to the Einstein-Hilbert action are quadratic
in the curvature invariants and we focus on the weak-field limit. We quantify
nonlocal quantum correlations by means of the violation of the
Clauser-Horne-Shimony-Holt inequality, and show how a curved background
suppresses the violation by a leading term due to general relativity and a
further contribution due to the corrections to Einstein gravity. Our results
can be generalized to massless particles such as photon pairs and can thus be
suitably exploited to devise precise experimental tests of extended models of
gravity.
