# Supersymmetric hybrid inflation with non-minimal coupling to gravity

## TL;DR

This paper explores a supersymmetric hybrid inflation model with non-minimal gravity coupling, showing it can fit current cosmological data and predicting specific parameter ranges and testable equations for future observations.

## Contribution

It introduces a supersymmetric hybrid inflation model with a non-minimal coupling to gravity that aligns with recent observational data and derives testable constraint equations.

## Key findings

- Model fits Planck and BICEP2/Keck data within a specific coupling range.
- Most probable non-minimal coupling value is approximately 0.0134.
- Predicted tensor-to-scalar ratio r is below current upper limits.

## Abstract

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.