A note on supergravity inflation in braneworld

Abstract

We discuss supergravity inflation in braneworld cosmology for the class of potentials $V(\varphi )=\alpha {\varphi }^n\exp (-{\beta }^{\mathrm{m}}{\varphi }^{\mathrm{m}})$ 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 $\Delta \varphi <1$.

Comments: 11 pages, 4 figures