241 research outputs found
An exact Jacobi map in the geodesic light-cone gauge
The remarkable properties of the recently proposed geodesic light-cone (GLC)
gauge allow to explicitly solve the geodetic-deviation equation, and thus to
derive an exact expression for the Jacobi map J^A_B(s,o) connecting a generic
source s to a geodesic observer o in a generic space time. In this gauge J^A_B
factorizes into the product of a local quantity at s times one at o, implying
similarly factorized expressions for the area and luminosity distance. In any
other coordinate system J^A_B is simply given by expressing the GLC quantities
in terms of the corresponding ones in the new coordinates. This is explicitly
done, at first and second order, respectively, for the synchronous and Poisson
gauge-fixing of a perturbed, spatially-flat cosmological background, and the
consistency of the two outcomes is checked. Our results slightly amend previous
calculations of the luminosity-redshift relation and suggest a possible
non-perturbative way for computing the effects of inhomogeneities on
observations based on light-like signals.Comment: 26 pages, no figures. Inconsequential modification of an equation,
comments and references added. Version accepted for publication in JCA
A new approach to the propagation of light-like signals in perturbed cosmological backgrounds
We present a new method to compute the deflection of light rays in a
perturbed FLRW geometry. We exploit the properties of the Geodesic Light Cone
(GLC) gauge where null rays propagate at constant angular coordinates
irrespectively of the given (inhomogeneous and/or anisotropic) geometry. The
gravitational deflection of null geodesics can then be obtained, in any other
gauge, simply by expressing the angular coordinates of the given gauge in terms
of the GLC angular coordinates. We apply this method to the standard Poisson
gauge, including scalar perturbations, and give the full result for the
deflection effect in terms of the direction of observation and observed
redshift up to second order, and up to third order for the leading lensing
terms. We also compare our results with those presently available in the
literature and, in particular, we provide a new non trivial check of a previous
result on the luminosity-redshft relation up to second order in cosmological
perturbation theory.Comment: 37 pages, no figures. Typos corrected, comments and references added.
Version accepted for publication in JCA
Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time
We study the renormalized energy-momentum tensor of gravitons in a de Sitter
space-time. After canonically quantizing only the physical degrees of freedom,
we adopt the standard adiabatic subtraction used for massless minimally coupled
scalar fields as a regularization procedure and find that the energy density of
gravitons in the E(3) invariant vacuum is proportional to H^4, where H is the
Hubble parameter, but with a positive sign. According to this result the scalar
expansion rate, which is gauge invariant in de Sitter space-time, is increased
by the fluctuations. This implies that gravitons may then add to conformally
coupled matter in driving the Starobinsky model of inflation.Comment: 5 pages, revtex, final version accepted for publication in PR
Stochastic growth of quantum fluctuations during slow-roll inflation
We compute the growth of the mean square of quantum fluctuations of test
fields with small effective mass during a slowly changing, nearly de Sitter
stage which took place in different inflationary models. We consider a
minimally coupled scalar with a small mass, a modulus with an effective mass (with as the Hubble parameter) and a massless non-minimally
coupled scalar in the test field approximation and compare the growth of their
relative mean square with the one of gauge-invariant inflaton fluctuations. We
find that in most of the single field inflationary models the mean square gauge
invariant inflaton fluctuation grows {\em faster} than any test field with a
non-negative effective mass. Hybrid inflationary models can be an exception:
the mean square of a test field can dominate over the gauge invariant inflaton
fluctuation one on suitably choosing parameters. We also compute the stochastic
growth of quantum fluctuation of a second field, relaxing the assumption of its
zero homogeneous value, in a generic inflationary model; as a main result, we
obtain that the equation of motion of a gauge invariant variable associated,
order by order, with a generic quantum scalar fluctuation during inflation can
be obtained only if we use the number of e-folds as the time variable in the
corresponding Langevin and Fokker-Planck equations for the stochastic approach.
We employ this approach to derive some bounds in the case of a model with two
massive fields.Comment: 9 pages, 4 figures. Added references, minor changes, matches the
version to be published in Phys. Rev.
Primordial black holes formation in a early matter dominated era from the pre-big bang scenario
We discuss the production of primordial black holes in an early matter
dominated era, which typically takes place in string inspired early universe
cosmological models. In particular, we consider a pre-big bang scenario
(extending previous results regarding formation in the radiation dominated era)
where the enhancement of curvature perturbations is induced by a variation of
the sound-speed parameter c_s during the string phase of high-curvature
inflation. After imposing all relevant observational constraints, we find that
the considered class of models is compatible with the production of a large
amount of primordial black holes, in the mass range relevant to dark matter,
only for a small range of the parameters space. On the other hand, we find that
a huge production of light primordial black holes may occur both in such matter
dominated era and in the radiation dominated one.Comment: 7 pages, 3 figure
Do stochastic inhomogeneities affect dark-energy precision measurements?
The effect of a stochastic background of cosmological perturbations on the
luminosity-redshift relation is computed to second order through a recently
proposed covariant and gauge-invariant light-cone averaging procedure. The
resulting expressions are free from both ultraviolet and infrared divergences,
implying that such perturbations cannot mimic a sizable fraction of dark
energy. Different averages are estimated and depend on the particular function
of the luminosity distance being averaged. The energy flux, being minimally
affected by perturbations at large z, is proposed as the best choice for
precision estimates of dark-energy parameters. Nonetheless, its irreducible
(stochastic) variance induces statistical errors on \Omega_{\Lambda}(z)
typically lying in the few-percent range.Comment: 5 pages, 3 figures. Comments and references added. Typos corrected.
Version accepted for publication in Phys. Rev. Let
Primordial Black Holes from Pre-Big Bang inflation
We discuss the possibility of producing a significant fraction of dark matter
in the form of primordial black holes in the context of the pre-big bang
inflationary scenario. We take into account, to this purpose, the enhancement
of curvature perturbations possibly induced by a variation of the sound-speed
parameter during the string phase of high-curvature inflation. After
imposing all relevant observational constraints, we find that the considered
class of models is compatible with the production of a large amount of
primordial black holes in the mass range relevant to dark matter, provided the
sound-speed parameter is confined in a rather narrow range of values, .Comment: 26 pages, two figures. Many new references and a few comments added.
Version accepted for publication in JCA
Second Order Gauge-Invariant Perturbations during Inflation
The evolution of gauge invariant second-order scalar perturbations in a
general single field inflationary scenario are presented. Different second
order gauge invariant expressions for the curvature are considered. We evaluate
perturbatively one of these second order curvature fluctuations and a second
order gauge invariant scalar field fluctuation during the slow-roll stage of a
massive chaotic inflationary scenario, taking into account the deviation from a
pure de Sitter evolution and considering only the contribution of super-Hubble
perturbations in mode-mode coupling. The spectra resulting from their
contribution to the second order quantum correlation function are nearly
scale-invariant, with additional logarithmic corrections to the first order
spectrum. For all scales of interest the amplitude of these spectra depend on
the total number of e-folds. We find, on comparing first and second order
perturbation results, an upper limit to the total number of e-folds beyond
which the two orders are comparable.Comment: 17 pages, 6 figures. Final version to appear in Phys. Rev.
Nonparametric Pooling And Testing Of Preference Ratings For Full-Profile Conjoint Analysis Experiments
The problem of pooling customer preference ratings within a conjoint analysis experiment has been addressed. A method based on the nonparametric combination of rankings has been proposed to compete with the usual method based on the arithmetic mean. This method is nonparametric with respect to the underlying dependence structure and so no dependence model must be assumed. The two methods have been compared using Spearman’s rank correlation coefficient and related test. Moreover, a further nonparametric testing method has been considered and proposed; this method takes both correlation and distance between ranks into account. By means of a simulation study it has been shown that the NPC Ranking method performs better than the arithmetic mean
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