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., the model can accommodate the inflation data reported by the Planck (ns and upper limit of r) and BICEP2/Keck (upper limit of r) collaborations. The study shows that the most probable value of. should be 0.0134 +/- 0.0005. That is coupling is found to be very weak. Within this range of., 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 ns 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 nsk and its running nskk 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.