Gravity Waves From Non-Minimal Quadratic Inflation

Abstract

We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter cR, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index ns, tensor-to-scalar ratio r=(2-4)x10^-3, and an inflaton mass close to 3x10^13 GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kahler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kahler manifold exhibits a no-scale-type symmetry, the model predicts ns=0.963 and r=0.004. Beyond no-scale SUGRA, ns and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kahler potential, and the prefactor encountered in it. Increasing slightly the latter above (-3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5-9)x10^13 GeV.