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 certain ranges of values of the non-minimal coupling parameter \xi , the model can accommodate the inflation data reported by the BICEP2 experiment as well as the data on the upper limit of the tensor-to-scalar ratio r set by the Planck and BICEP2/Keck collaborations .
The study shows that the most probable value of \xi should be \sim 0.0046 \pm 0.0005 .
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 lay 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 derivations of the constraint equations for the running of the scalar spectral index n _ { sk } and its running n _ { skk } from our model prove the ingenuine mathematical structure of it .
These equations can be used to test our model from the data of future cosmological observations .