2,006 research outputs found
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
L^p-summability of Riesz means for the sublaplacian on complex spheres
In this paper we study the L^p-convergence of the Riesz means for the
sublaplacian on the sphere S^{2n-1} in the complex n-dimensional space C^n. We
show that the Riesz means of order delta of a function f converge to f in
L^p(S^{2n-1}) when delta>delta(p):=(2n-1)|1\2-1\p|. The index delta(p) improves
the one found by Alexopoulos and Lohoue', 2n|1\2-1\p|, and it coincides with
the one found by Mauceri and, with different methods, by Mueller in the case of
sublaplacian on the Heisenberg group.Comment: Rapporto interno Politecnico di Torino, Novembre 200
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
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