Anisotropic Inflation with Derivative Couplings

Abstract

We study anisotropic inflationary solutions when the inflaton and its derivative couple to a vector field. This type of coupling is motivated by D-brane inflationary models, in which the inflaton, and a vector field living on the D-brane, couple disformally (derivatively). We start by studying a phenomenological model where we show the existence of anisotropic solutions and demonstrate their stability via a dynamical system analysis. Compared to the case without a derivative coupling, the anisotropy is reduced and thus can be made consistent with current limits, while the value of the slow-roll parameter remains almost unchanged. We also discuss solutions for more general cases, including D-brane like couplings.

15 pages, 2 figures. References added, typos and minor errors corrected. Improved discussion on solutions. Version to appear in PRD