  We investigate the entanglement due to geometric corrections in particle
creation during inflation. To do so, we propose a single-field inflationary
scenario, nonminimally coupled to the scalar curvature of spacetime. We require
particle production to be purely geometric, setting to zero the Bogolubov
coefficients and computing the $S$ matrix associated to spacetime
perturbations, which are traced back to inflaton fluctuations. The
corresponding particle density leads to a nonzero entanglement entropy whose
effects are investigated at primordial time of Universe evolution. The
possibility of modeling our particle candidate in terms of dark matter is
discussed. The classical back-reaction of inhomogeneities on the homogeneous
dynamical background degrees of freedom is also studied and quantified in the
slow-roll regime.
