1,258 research outputs found
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 and its truncated version
. 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 and find a sufficient condition for its solution.Comment: 14 pages, Author Accepted Manuscrip
Production of Massive Fermions at Preheating and Leptogenesis
We present a complete computation of the inflaton decay into very massive
fermions during preheating. We show that heavy fermions are produced very
efficiently up to masses of order 10^{17}-10^{18} GeV; the accessible mass
range is thus even broader than the one for heavy bosons. We apply our findings
to the leptogenesis scenario, proposing a new version of it, in which the
massive right-handed neutrinos, responsible for the generation of the baryon
asymmetry, are produced during preheating. We also discuss other production
mechanisms of right-handed neutrinos in the early Universe, identifying the
neutrino mass parameters for which the observed baryon asymmetry is reproduced.Comment: 29 pages, 4 figure
Measurement of Parity Violation in the Early Universe using Gravitational-wave Detectors
A stochastic gravitational-wave background (SGWB) is expected to arise from
the superposition of many independent and unresolved gravitational-wave
signals, of either cosmological or astrophysical origin. Some cosmological
models (characterized, for instance, by a pseudo-scalar inflaton, or by some
modification of gravity) break parity, leading to a polarized SGWB. We present
a new technique to measure this parity violation, which we then apply to the
recent results from LIGO to produce the first upper limit on parity violation
in the SGWB, assuming a generic power-law SGWB spectrum across the LIGO
sensitive frequency region. We also estimate sensitivity to parity violation of
the future generations of gravitational-wave detectors, both for a power-law
spectrum and for a model of axion inflation. This technique offers a new way of
differentiating between the cosmological and astrophysical sources of the
isotropic SGWB, as astrophysical sources are not expected to produce a
polarized SGWB.Comment: 5 pages, 2 figures, 1 tabl
The Ineludible non-Gaussianity of the Primordial Black Hole Abundance
We study the formation of primordial black holes when they are generated by
the collapse of large overdensities in the early universe. Since the density
contrast is related to the comoving curvature perturbation by a nonlinear
relation, the overdensity statistics is unavoidably non-Gaussian. We show that
the abundance of primordial black holes at formation may not be captured by a
perturbative approach which retains the first few cumulants of the non-Gaussian
probability distribution. We provide two techniques to calculate the
non-Gaussian abundance of primordial black holes at formation, one based on
peak theory and the other on threshold statistics. Our results show that the
unavoidable non-Gaussian nature of the inhomogeneities in the energy density
makes it harder to generate PBHs. We provide simple (semi-)analytical
expressions to calculate the non-Gaussian abundances of the primordial black
holes and show that for both narrow and broad power spectra the gaussian case
from threshold statistics is reproduced by increasing the amplitude of the
power spectrum by a factor .Comment: 26 pages, 10 figures, matching published versio
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