29,035 research outputs found
Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy
We include the effect of neutrino free streaming into the spectrum of relic
gravitational waves (RGWs) in the currently accelerating universe. For the
realistic case of a varying fractional neutrino energy density and a
non-vanishing derivative of mode function at the neutrino decoupling, the
integro-differential equation of RGWs is solved by a perturbation method for
the period from the neutrino decoupling to the matter-dominant stage.
Incorporating it to the analytic solution of the whole history of expansion of
the universe, the analytic solution of GRWs is obtained, evolving from the
inflation up to the current acceleration. The resulting spectrum of GRWs covers
the whole range of frequency Hz, and improves the
previous results. It is found that the neutrino free-streaming causes a
reduction of the spectral amplitude by in the range Hz, and leaves the other portion of the spectrum almost unchanged.
This agrees with the earlier numerical calculations. Examination is made on the
difference between the accelerating and non-accelerating models, and our
analysis shows that the ratio of the spectral amplitude in accelerating
CDM model over that in CDM model is , and within the various
accelerating models of the spectral amplitude is
proportional to for the whole range of frequency.
Comparison with LIGO S5 Runs Sensitivity shows that RGWs are not yet detectable
by the present LIGO, and in the future LISA may be able to detect RGWs in some
inflationary models.Comment: 22 pages,12 figures, accepeted by PR
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
Effects of cold dark matter decoupling and pair annihilation on cosmological perturbations
Weakly interacting massive particles are part of the lepton-photon plasma in
the early universe until kinetic decoupling, after which time the particles
behave like a collisionless gas with nonzero temperature. The Boltzmann
equation for WIMP-lepton collisions is reduced to a Fokker-Planck equation for
the evolution of the WIMP distribution including scalar density perturbations.
This equation and the Einstein and fluid equations for the plasma are solved
numerically including the acoustic oscillations of the plasma before and during
kinetic decoupling, the frictional damping occurring during kinetic decoupling,
and the free-streaming damping occurring afterwards and throughout the
radiation-dominated era. An excellent approximation reduces the solution to
quadratures for the cold dark matter density and velocity perturbations. The
subsequent evolution is followed through electron pair annihilation and the
radiation-matter transition; analytic solutions are provided for both large and
small scales. For a 100 GeV WIMP with bino-type interactions, kinetic
decoupling occurs at a temperature MeV. The transfer function in the
matter-dominated era leads to an abundance of small cold dark matter halos;
with a smooth window function the Press-Schechter mass distribution is for 10 MeV) M.Comment: 18 pages, 12 figures; corrected error in bino decoupling temperature,
figures update
Dilepton production from a viscous QGP
This work calculates the first correction to the leading order q\={q}
dilepton production rates due to shear viscosity in an expanding gas. The
modified rates are integrated over the space-time history of a viscous
hydrodynamic simulation of RHIC collisions. The net result is a {\em hardening}
of spectrum with the magnitude of the correction increasing with
invariant mass. We argue that a thermal description is reliable for invariant
masses less than . For reasonable
values of the shear viscosity and thermalization time GeV.
Finally, the early emission from a viscous medium is compared to emission from
a longitudinally free streaming plasma. Qualitative differences in
spectrum are seen which could be used to extract information on the
thermalization time, viscosity to entropy ratio and possibly the thermalization
mechanism in heavy-ion collisions.Comment: 17 pages, 8 figure
Small scale aspects of warm dark matter : power spectra and acoustic oscillations
We provide a semi-analytic study of the small scale aspects of the power
spectra of warm dark matter (WDM) candidates that decoupled while relativistic
with arbitrary distribution functions. These are characterized by two widely
different scales and k_{fs}=
\sqrt{3}\,k_{eq}/2\,^{1/2} with the
velocity dispersion at matter radiation equality. Density perturbations evolve
through three stages: radiation domination when the particle is relativistic
and non-relativistic and matter domination. An early ISW effect during the
first stage leads to an enhancement of density perturbations and a plateau in
the transfer function for . An effective fluid description
emerges at small scales which includes the effects of free streaming in initial
conditions and inhomogeneities. The transfer function features
\emph{WDM-acoustic oscillations} at scales . We study the
power spectra for two models of sterile neutrinos with
produced non-resonantly, at the QCD and EW scales respectively. The latter case
yields acoustic oscillations on mass scales . Our
results reveal a \emph{quasi-degeneracy} between the mass, distribution
function and decoupling temperature suggesting caveats on the constraints on
the mass of a sterile neutrino from current WDM N-body simulations and
Lyman- forest data. A simple analytic interpolation of the power
spectra between large and small scales and its numerical implementation is
given.Comment: 47 pages, 17 figures, section with comparison with Boltzmann code
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