Tachyon inflation in the Large-$N$ formalism

We study tachyon inflation within the large-$N$ formalism, which takes a prescription for the small Hubble flow slow--roll parameter $epsilon_1$ as a function of the large number of $e$-folds $N$. This leads to a classification of models through their behaviour at large $N$. In addition to the perturbative $N$ class, we introduce the polynomial and exponential classes for the $epsilon_1$ parameter. With this formalism we reconstruct a large number of potentials used previously in the literature for Tachyon Inflation. We also obtain new families of potentials form the polynomial class. We characterize the realizations of Tachyon Inflation by computing the usual cosmological observables up to second order in the Hubble flow slow--roll parameters. This allows us to look at observable differences between tachyon and canonical single field inflation. The analysis of observables in light of the Planck 2015 data shows the viability of some of these models, mostly for certain realization of the polynomial and exponential classes.

Mass hierarchy, mass gap and corrections to Newtons law on thick branes with Poincare symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newtons law in the thin brane limit. In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the (thin) Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved as in the Lykken-Randall model and the model is completely free of naked singularities.