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 c(R), 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 n(s), tensor-to-scalar ratio r similar or equal to (2 – 4) . 10(-3), and an inflaton mass close to 3 . 10 (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 n(s) similar or equal to 0.963 and r similar or equal to 0.004. Beyond no-scale SUGRA, n(s) 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) . 10(13) GeV.

Abstract: In the framework of Born-Infeld inspired gravity theories, which deviates from General Relativity (GR) in the high curvature regime, we discuss the viability of Cosmic Inflation without scalar fields. For energy densities higher than the new mass scale of the theory, a gravitating (lust component is shown to generically induce an accelerated expansion of the Universe. Within such a simple scenario, inflation gracefiffly exits when the CR regime is recovered, but the Universe would remain matter dominated. In order to implement a reheating era after inflation, we then consider inflation to be driven by a mixture of unstable dust species decaying into radiation. Because the speed of sound gravitates within the BornInfeld model under consideration, our scenario ends up being predictive on various open questions of the inflationary paradigm. The total number of e-folds of acceleration is given by the lifetime of the unstable dust components and is related to the duration of reheating. As a result, inflation does not last much longer than the number of e-folds of deceleration allowing a small spatial curvature and large scale deviations to isotropy to be observable today. Energy densities are self-regulated as inflation can only start for a total energy density less than a threshold value, again related to the species' lifetime. Above this threshold, the Universe may bc nee thereby avoiding a singularity. Another distinctive feature is that the accelerated expansion is of the superinflationary ldnd, namely the first Hubble flow function is negative. We show however that the tensor modes are never excited and the tensor-to-scalar ratio is always vanishing, independently of the energy scale of inflation.