Vector inflation by kinetic coupled gravity

Vector inflation is a newly established model where inflation is driven by non-minimally coupled massive vector fields with a potential term. This model is similar to the model of chaotic inflation with scalar fields, except that for vector fields the isotropy of expansion is achieved either by considering a triplet of orthogonal vector fields or $N$ randomly oriented independent vector fields. We introduce a new version of vector inflation where the vector field has no potential term but is non-minimally coupled to gravity through the kinetic term. The non-minimal coupling is established by introducing the Einstein tensor besides the metric tensor within the kinetic term of the vector field.