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The superpotential method is a reconstruction technique which has proven useful to build exact cosmological solutions. We here employ the superpotential method in order to reconstruct the features necessary for the inflaton potential to drive inflation and lead to the amplification of the curvature perturbations. Such an amplification, at wavelengths shorter than those observed in the CMB, is necessary in order to have a significant formation of Primordial Black Holes after inflation ends. The technique is applied to the cases of a minimally coupled inflaton, to the non-minimal coupling case and to f(R) theories of gravity. For such theories, a model dependent analysis of the features leading to the scalar spectrum enhancement is also presented., Comment: 30 pages

We study a possible amplification mechanism for the curvature perturbations generated during inflation by a Dirac-Born-Infeld (DBI) inflaton in the presence of a sharp feature in the warp factor. The large growth resulting in the scalar power spectrum is a consequence of the decreasing speed of sound. We obtain analytical approximate expressions for the relevant dynamical quantities both in the slow roll phase and during the transient phase which leads to the amplification. We finally compare our approximations to the exact numerical evolution and give, in such a context, the general rules for building a viable inflationary model leading to, during the subsequent radiation dominated era, an abundant primordial black holes formation., Comment: 27 pages, 5 figures. Final version accepted for publication on JCAP

We study a mechanism for the amplification of the inflationary scalar perturbation when the inflaton field action is non-canonical, i.e. the inflaton kinetic term has a non-standard form. For such a case the speed of sound of the perturbations generated during inflation is less than one and in general changes with time. Furthermore in such models, even when the scalar field potential is negligible, diverse inflationary attractors may exist. The possible effects of a speed of sound approaching zero during some stage of inflation may lead to a large amplification for the amplitude of the scalar spectrum which, on horizon re-entry during the radiation dominated phase, can collapse and form primordial black holes (PBH) of a mass $M_{\rm BH}\sim 10^{-15}M_{\odot}$ which may constitute a large fraction of the total Dark Matter (DM) today., Comment: 14 pages, 1 figure. References added. Final version published on PLB

We illustrate how it is possible to calculate the quantum gravitational effects on the spectra of primordial scalar/tensor perturbations starting from the canonical, Wheeler-De Witt, approach to quantum cosmology. The composite matter-gravity system is analysed through a Born-Oppenheimer approach in which gravitation is associated with the heavy degrees of freedom and matter (here represented by a scalar field) with the light ones. Once the independent degrees of freedom are identified the system is canonically quantised. The differential equation governing the dynamics of the primordial spectra with its quantum-gravitational corrections is then obtained and is applied to diverse inflationary evolutions. Finally, the analytical results are compared to observations through a Monte Carlo Markov Chain technique and an estimate of the free parameters of our approach is finally presented and the results obtained are compared with previous ones., Comment: 42 pages, 4 figures

The conditions for the cancellation of one loop contributions to vacuum energy (both U.V. divergent and finite) coming from the known (Standard Model) fields and the field associated with the hypothetical 750 Gev diphoton excess are examined. Depending on the nature of this latter resonance we find that in order to satisfy the constraints (sum rules) different additional, minimal field contributions are required, leading to yet to be observed particles., Comment: 24 pages, 4 figures. arXiv admin note: text overlap with arXiv:0804.4782

The spectrum of primordial perturbations obtained by calculating the quantum gravitational corrections to the dynamics of scalar perturbations is compared with Planck 2013 and BICEP2/{\it Keck Array} public data. The quantum gravitational effects are calculated in the context of a Wheeler-De Witt approach and have quite distinctive features. We constrain the free parameters of the theory by comparison with observations., Comment: 17 pages, 3 figures; the analysis has been updated with the combined Planck-BICEP2/Keck Array public data. Final version, accepted for publication in JCAP