489 research outputs found
On localization properties of Fourier transforms of hyperfunctions
In [Adv. Math. 196 (2005) 310-345] the author introduced a new generalized
function space which can be naturally interpreted as the
Fourier transform of the space of Sato's hyperfunctions on . It was shown
that all Gelfand--Shilov spaces () of
analytic functionals are canonically embedded in . While the
usual definition of support of a generalized function is inapplicable to
elements of and , their
localization properties can be consistently described using the concept of {\it
carrier cone} introduced by Soloviev [Lett. Math. Phys. 33 (1995) 49-59; Comm.
Math. Phys. 184 (1997) 579-596]. In this paper, the relation between carrier
cones of elements of and is
studied. It is proved that an analytic functional is carried by a cone if and only if its
canonical image in is carried by .Comment: 21 pages, final version, accepted for publication in J. Math. Anal.
App
Cosmological Constraints from calibrated Yonetoku and Amati relation implies Fundamental plane of Gamma-ray bursts
We consider two empirical relations using data only from the prompt emission
of Gamma-Ray Bursts (GRBs), peak energy () - peak luminosity ()
relation (so called Yonetoku relation) and -isotropic energy () relation (so called Amati relation). We first suggest the independence
of the two relations although they have been considered similar and dependent.
From this viewpoint, we compare constraints on cosmological parameters,
and , from the Yonetoku and Amati relations
calibrated by low-redshift GRBs with . We found that they are
different in 1- level, although they are still consistent in 2-
level. This and the fact that both Amati and Yonetoku relations have systematic
errors larger than statistical errors suggest the existence of a hidden
parameter of GRBs. We introduce the luminosity time defined by as a hidden parameter to obtain a generalized Yonetoku
relation as . The new relation has much smaller systematic
error, 30%, and can be regarded as "Fundamental plane" of GRBs. We show a
possible radiation model for this new relation. Finally we apply the new
relation for high-redshift GRBs with to obtain
, which is consistent with the
concordance cosmological model within 2- level.Comment: 5 pages, 6 figures, published in JCA
High-Redshift Cosmography
We constrain the parameters describing the kinematical state of the universe
using a cosmographic approach, which is fundamental in that it requires a very
minimal set of assumptions (namely to specify a metric) and does not rely on
the dynamical equations for gravity. On the data side, we consider the most
recent compilations of Supernovae and Gamma Ray Bursts catalogues. This allows
to further extend the cosmographic fit up to , i.e. up to redshift for
which one could start to resolve the low z degeneracy among competing
cosmological models. In order to reliably control the cosmographic approach at
high redshifts, we adopt the expansion in the improved parameter .
This series has the great advantage to hold also for and hence it is
the appropriate tool for handling data including non-nearby distance
indicators. We find that Gamma Ray Bursts, probing higher redshifts than
Supernovae, have constraining power and do require (and statistically allow) a
cosmographic expansion at higher order than Supernovae alone. Exploiting the
set of data from Union and GRBs catalogues, we show (for the first time in a
purely cosmographic approach parametrized by deceleration , jerk ,
snap ) a definitively negative deceleration parameter up to the
3 confidence level. We present also forecasts for realistic data sets
that are likely to be obtained in the next few years.Comment: 16 pages, 6 figures, 3 tables. Improved version matching the
published one, additional comments and reference
Early Dark Energy at High Redshifts: Status and Perspectives
Early dark energy models, for which the contribution to the dark energy
density at high redshifts is not negligible, influence the growth of cosmic
structures and could leave observable signatures that are different from the
standard cosmological constant cold dark matter (CDM) model. In this
paper, we present updated constraints on early dark energy using geometrical
and dynamical probes. From WMAP five-year data, baryon acoustic oscillations
and type Ia supernovae luminosity distances, we obtain an upper limit of the
dark energy density at the last scattering surface (lss), (95% C.L.). When we include higher redshift
observational probes, such as measurements of the linear growth factors,
Gamma-Ray Bursts (GRBs) and Lyman- forest (\lya), this limit improves
significantly and becomes (95%
C.L.). Furthermore, we find that future measurements, based on the
Alcock-Paczy\'nski test using the 21cm neutral hydrogen line, on GRBs and on
the \lya forest, could constrain the behavior of the dark energy component and
distinguish at a high confidence level between early dark energy models and
pure CDM. In this case, the constraints on the amount of early dark
energy at the last scattering surface improve by a factor ten, when compared to
present constraints. We also discuss the impact on the parameter , the
growth rate index, which describes the growth of structures in standard and in
modified gravity models.Comment: 11 pages, 9 figures and 4 table
The Large Magellanic Cloud and the Distance Scale
The Magellanic Clouds, especially the Large Magellanic Cloud, are places
where multiple distance indicators can be compared with each other in a
straight-forward manner at considerable precision. We here review the distances
derived from Cepheids, Red Variables, RR Lyraes, Red Clump Stars and Eclipsing
Binaries, and show that the results from these distance indicators generally
agree to within their errors, and the distance modulus to the Large Magellanic
Cloud appears to be defined to 3% with a mean value of 18.48 mag, corresponding
to 49.7 Kpc. The utility of the Magellanic Clouds in constructing and testing
the distance scale will remain as we move into the era of Gaia.Comment: 23 pages, accepted for publication in Astrophysics and Space Science.
From a presentation at the conference The Fundamental Cosmic Distance Scale:
State of the Art and the Gaia Perspective, Naples, May 201
Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories
We present cosmological perturbations of kinetic components based on
relativistic Boltzmann equations in the context of generalized gravity
theories. Our general theory considers an arbitrary number of scalar fields
generally coupled with the gravity, an arbitrary number of mutually interacting
hydrodynamic fluids, and components described by the relativistic Boltzmann
equations like massive/massless collisionless particles and the photon with the
accompanying polarizations. We also include direct interactions among fluids
and fields. The background FLRW model includes the general spatial curvature
and the cosmological constant. We consider three different types of
perturbations, and all the scalar-type perturbation equations are arranged in a
gauge-ready form so that one can implement easily the convenient gauge
conditions depending on the situation. In the numerical calculation of the
Boltzmann equations we have implemented four different gauge conditions in a
gauge-ready manner where two of them are new. By comparing solutions solved
separately in different gauge conditions we can naturally check the numerical
accuracy.Comment: 26 pages, 9 figures, revised thoroughly, to appear in Phys. Rev.
Protocols, methods, and tools for genome-wide association studies (GWAS) of dental traits
Oral health and disease are known to be influenced by complex interactions between environmental (e.g., social and behavioral) factors and innate susceptibility. Although the exact contribution of genomics and other layers of “omics” to oral health is an area of active research, it is well established that the susceptibility to dental caries, periodontal disease, and other oral and craniofacial traits is substantially influenced by the human genome. A comprehensive understanding of these genomic factors is necessary for the realization of precision medicine in the oral health domain. To aid in this direction, the advent and increasing affordability of high-throughput genotyping has enabled the simultaneous interrogation of millions of genetic polymorphisms for association with oral and craniofacial traits. Specifically, genome-wide association studies (GWAS) of dental caries and periodontal disease have provided initial insights into novel loci and biological processes plausibly implicated in these two common, complex, biofilm-mediated diseases. This paper presents a summary of protocols, methods, tools, and pipelines for the conduct of GWAS of dental caries, periodontal disease, and related traits. The protocol begins with the consideration of different traits for both diseases and outlines procedures for genotyping, quality control, adjustment for population stratification, heritability and association analyses, annotation, reporting, and interpretation. Methods and tools available for GWAS are being constantly updated and improved; with this in mind, the presented approaches have been successfully applied in numerous GWAS and meta-analyses among tens of thousands of individuals, including dental traits such as dental caries and periodontal disease. As such, they can serve as a guide or template for future genomic investigations of these and other traits
Toward an internally consistent astronomical distance scale
Accurate astronomical distance determination is crucial for all fields in
astrophysics, from Galactic to cosmological scales. Despite, or perhaps because
of, significant efforts to determine accurate distances, using a wide range of
methods, tracers, and techniques, an internally consistent astronomical
distance framework has not yet been established. We review current efforts to
homogenize the Local Group's distance framework, with particular emphasis on
the potential of RR Lyrae stars as distance indicators, and attempt to extend
this in an internally consistent manner to cosmological distances. Calibration
based on Type Ia supernovae and distance determinations based on gravitational
lensing represent particularly promising approaches. We provide a positive
outlook to improvements to the status quo expected from future surveys,
missions, and facilities. Astronomical distance determination has clearly
reached maturity and near-consistency.Comment: Review article, 59 pages (4 figures); Space Science Reviews, in press
(chapter 8 of a special collection resulting from the May 2016 ISSI-BJ
workshop on Astronomical Distance Determination in the Space Age
Reconstructing the Cosmic Expansion History up to Redshift z=6.29 with the Calibrated Gamma-Ray Bursts
Recently, Gamma-Ray Bursts (GRBs) were proposed to be a complementary
cosmological probe to type Ia supernovae (SNIa). GRBs have been advocated to be
standard candles since several empirical GRB luminosity relations were proposed
as distance indicators. However, there is a so-called circularity problem in
the direct use of GRBs. Recently, a new idea to calibrate GRBs in a completely
cosmology independent manner has been proposed, and the circularity problem can
be solved. In the present work, following the method proposed by Liang {\it et
al.}, we calibrate 70 GRBs with the Amati relation using 307 SNIa. Then,
following the method proposed by Shafieloo {\it et al.}, we smoothly
reconstruct the cosmic expansion history up to redshift with the
calibrated GRBs. We find some new features in the reconstructed results.Comment: 12 pages, 4 figures, 1 table, revtex4; v2: title changed, accepted by
Eur. Phys. J. C; v3: published versio
Testing a Phenomenologically Extended DGP Model with Upcoming Weak Lensing Surveys
A phenomenological extension of the well-known brane-world cosmology of
Dvali, Gabadadze and Porrati (eDGP) has recently been proposed. In this model,
a cosmological-constant-like term is explicitly present as a non-vanishing
tension sigma on the brane, and an extra parameter alpha tunes the cross-over
scale r_c, the scale at which higher dimensional gravity effects become non
negligible. Since the Hubble parameter in this cosmology reproduces the same
LCDM expansion history, we study how upcoming weak lensing surveys, such as
Euclid and DES (Dark Energy Survey), can confirm or rule out this class of
models. We perform Markov Chain Monte Carlo simulations to determine the
parameters of the model, using Type Ia Supernov\ae, H(z) data, Gamma Ray Bursts
and Baryon Acoustic Oscillations. We also fit the power spectrum of the
temperature anisotropies of the Cosmic Microwave Background to obtain the
correct normalisation for the density perturbation power spectrum. Then, we
compute the matter and the cosmic shear power spectra, both in the linear and
non-linear regimes. The latter is calculated with the two different approaches
of Hu and Sawicki (2007) (HS) and Khoury and Wyman (2009) (KW). With the eDGP
parameters coming from the Markov Chains, KW reproduces the LCDM matter power
spectrum at both linear and non-linear scales and the LCDM and eDGP shear
signals are degenerate. This result does not hold with the HS prescription:
Euclid can distinguish the eDGP model from LCDM because their expected power
spectra roughly differ by the 3sigma uncertainty in the angular scale range
700<l<3000; on the contrary, the two models differ at most by the 1sigma
uncertainty over the range 500<l<3000 in the DES experiment and they are
virtually indistinguishable.Comment: 22 pages, 5 figures, 4 tables, JCAP in pres
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