  This paper is a part of a series devoted to the Euclidean-hyperboloidal
foliation method introduced by the authors for investigating the global
existence problem associated with nonlinear systems of coupled
wave-Klein-Gordon equations with small data. This method was developed
especially for investigating the initial value problem for the Einstein-massive
field system in wave gauge. Here, we study the (fourth-order) field equations
of f(R) modified gravity and investigate the global dynamical behavior of the
gravitational field in the near-Minkowski regime. We establish the existence of
a globally hyperbolic Cauchy development approaching Minkowski spacetime (in
spacelike, null, and timelike directions), when the initial data set is
sufficiently close to an asymptotically Euclidean and spacelike hypersurface in
Minkowski spacetime. We cast the (fourth-order) f(R)-field equations in the
form of a second-order wave-Klein-Gordon system, which has an analogous
structure to the Einstein-massive field system but, in addition, involves a
(possibly small) effective mass parameter. We establish the nonlinear stability
of the Minkowski spacetime in the context of f(R) gravity, when the integrand
f(R) in the action functional can be taken to be arbitrarily close to the
integrand R of the standard Hilbert-Einstein action.
