Behavior of chaotic inflation in anisotropic cosmologies with nonminimal coupling

Abstract

We review the behavior of the chaotic inflationary scenario in the minimally coupled anisotropic case and in the nonminimally coupled isotropic case. In the former, anisotropy enhances inflation. In the latter, positive nonminimal coupling introduces a singularity at a critical point \ensuremath{\varphi}${^}_{c}$ in the scalar field. The exact value of \ensuremath{\varphi}${^}_{c}$ depends on the coupling parameter \ensuremath{\xi}. This singularity cannot be exceeded, which precludes astrophysically sufficient inflation for \ensuremath{\xi}\ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}2}$. We extend the analysis to anisotropic Bianchi models where a second singularity ${\ensuremath{\varphi}}_{c}$ appears, which further prevents inflation in these models for \ensuremath{\xi}\ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}2}$.