Preheating of massive fermions after inflation: analytical results

Non-perturbative production of fermions after chaotic inflation has been the object of several studies in the very recent past. However, the results in the most interesting case of production of massive fermions in an expanding Universe were so far known only numerically. We provide very simple and readable analytical formulae, both for the spectra of the created fermions and for their total energy density. Their derivation is closely related to the one adopted for bosons and exploits the fact that the production occurs during very short intervals of nonadiabatical change of the fermionic frequency. Our formulae show the presence of resonance bands if the expansion of the Universe is neglected, and their disappearance when the latter is included. As in the bosonic case, this last effect is due to the stochastic character that the expansion gives to the whole process. Backreaction is considered in the last part of the work. All our analytical results are in excellent agreement with the previous numerical ones in the regime of validity of the latter. However, a more accurate scaling for the energy density of the produced fermions is here found.Comment: Final version, 31 pages, 9 figure

Stability analysis of 5D gravitational solutions with N bulk scalar fields

We study the stability of 5D gravitational solutions containing an arbitrary number of scalar fields. A closed set of equations is derived which governs the background and perturbations of N scalar fields and the metric, for arbitrary bulk and boundary scalar potentials. In particular the effect of the energy-momentum tensor of the scalar fields on the geometry is fully taken into account, together with all the perturbations of the system. The equations are explicitly written as an eigenvalue problem, which can be readily solved to determine the stability of the system and obtain the properties of the fluctuations, such as masses and couplings. As an example, we study a dynamical soft-wall model with two bulk scalar fields used to model the hadron spectrum of QCD and the Higgs sector of electroweak physics. It is shown that there are no tachyonic modes, and that there is a (radion) mode whose mass is suppressed by a large logarithm compared to that of the other Kaluza-Klein modes.Comment: 15 pages, 5 figures. v2: refs adde

Completeness on the worm domain and the M\"untz-Sz\'asz problem for the Bergman space

In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain $\mathcal{W}_\mu$ and its truncated version $\mathcal{W}'_\mu$. We determine some orthogonal systems and show that they are not complete, while showing that the union of two particular of such systems is complete. In order to prove our completeness result we introduce the Muentz-Szasz problem for the 1-dimensional Bergman space of the disk $\{\zeta : |\zeta-1|<1\}$ and find a sufficient condition for its solution.Comment: 14 pages, Author Accepted Manuscrip