Effective models of inflation from a non-local framework

Abstract

The dilaton is a possible inflaton candidate following recent CMB data allowing a non-minimal coupling to the Ricci curvature scalar in the early Universe. In this paper, we introduce an approach that has seldom been used in the literature, namely dilaton inflation with non-local features. More concretely, employing non-local features expressed in J. High Energy Phys. 04 (2007) 029, we study quadratic variations around a de Sitter geometry of an effective action with a non-local dilaton. The non-locality refers to an infinite derivative kinetic term involving the operator $\mathcal{F}\left(\Box\right)$. Algebraic roots of the characteristic equation $\mathcal{F}(z)=0$ play a crucial role in determining the properties of the theory. We subsequently study the cases when $\mathcal{F}\left(\Box\right)$ has one real root and one complex root, from which we retrieve two concrete effective models of inflation. In the first case we retrieve a class of single field inflations with universal prediction of $n_{s}\sim0.967$ with any value of the tensor to scalar ratio $r<0.1$ intrinsically controlled by the root of the characteristic equation. The second case involves a new class of two field conformally invariant models with a peculiar quadratic cross-product of scalar fields. In this latter case, we obtain Starobinsky like inflation through a spontaneously broken conformal invariance. Furthermore, an uplifted minimum of the potential, which accounts for the vacuum energy after inflation is produced naturally through this mechanism intrinsically within our approach.