Inflation from a nonlinear magnetic monopole field nonminimally coupled
  to curvature
  In the context of nonminimally coupled $f(R)$ gravity theories, we study
early inflation driven by a nonlinear monopole magnetic field which is
nonminimally coupled to curvature. In order to isolate the effects of the
nonminimal coupling between matter and curvature we assume the pure
gravitational sector to have the Einstein-Hilbert form. Thus, we study the most
simple model with a nonminimal coupling function which is linear in the Ricci
scalar. From an effective fluid description, we show the existence of an early
exponential expansion regime of the Universe, followed by a transition to a
radiation-dominated era. In particular, by applying the most recent results of
the Planck collaboration we set the limits on the parameter of the nonminimal
coupling, and the quotient of the nonminimal coupling and the nonlinear
monopole magnetic scales. We found that these parameters must take large values
in order to satisfy the observational constraints. Furthermore, by obtaining
the relation for the graviton mass, we show the consistency of our results with
the recent gravitational wave data GW$170817$ of LIGO and Virgo.
