Supersymmetric hybrid inflation with non-minimal coupling to gravity
  We have studied the paradigm of cosmic inflation using the simplest model
based on the idea of supersymmetric hybrid inflation with non-minimal coupling
to gravity, specially under the slow-roll approximation following the
superconformal approach to supergravity. It is found that within a range of
values of the non-minimal coupling parameter $\xi$, the model can accommodate
the inflation data reported by the Planck ($n_s$ and upper limit of $r$) and
BICEP2/Keck (upper limit of $r$) collaborations. The study shows that the most
probable value of $\xi$ should be $\sim 0.0134\pm0.0005$. That is coupling is
found to be very week. Within this range of $\xi$, the values of $r$ estimated
from our model for $50 - 70$ e-foldings are found to be laying well below the
upper limits set by the Planck and BICEP2/Keck collaborations. Similarly,
values of $n_s$ obtained for the said parameters are in good agreement with its
latest data of the Planck collaboration. The constraint equations for the
running of the scalar spectral index $n_{sk}$ and its running $n_{skk}$ are
derived from the numerical solutions of our model for these parameters. These
equations can be used to test our model from the data of future cosmological
observations.
