# A note on supergravity inflation in braneworld

## TL;DR

This paper explores supergravity inflation within braneworld cosmology using specific potentials, showing compatibility with observations and predicting sub-Planckian inflaton excursions due to high-energy corrections.

## Contribution

It introduces a class of minimal supergravity inflation models in braneworld scenarios that evade the eta problem and fit observational data, with analytic and numerical predictions for key inflationary parameters.

## Key findings

- Models with smaller n are observationally favored.
- High-energy corrections lead to sub-Planckian inflaton excursions.
- Predictions for spectral index and tensor-to-scalar ratio are provided.

## Abstract

We discuss supergravity inflation in braneworld cosmology for the class of potentials $V(\phi)=\alpha \phi^n\rm{exp}(-\beta^m \phi^m)$ with $m=1,~2$. These minimal SUGRA models evade the $\eta$ problem due to a broken shift symmetry and can easily accommodate the observational constraints. In the high energy regime $V/\lambda\gg 1$, the numerical predictions and approximate analytic formulas are given for the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$. The models with smaller $n$ are preferred while the models with larger $n$ are out of the $2\sigma$ region. Remarkably, the $\rho^2/\lambda$ correction to the energy density in Friedmann equation results in sub-Planckian inflaton excursions $\Delta\phi <1$.