615 research outputs found
Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics
We develop an efficient sampling method by simulating Langevin dynamics with
an artificial force rather than a natural force by using the gradient of the
potential energy. The standard technique for sampling following the
predetermined distribution such as the Gibbs-Boltzmann one is performed under
the detailed balance condition. In the present study, we propose a modified
Langevin dynamics violating the detailed balance condition on the
transition-probability formulation. We confirm that the numerical
implementation of the proposed method actually demonstrates two major
beneficial improvements: acceleration of the relaxation to the predetermined
distribution and reduction of the correlation time between two different
realizations in the steady state.Comment: 18pages, 3 figures, proceeedings of STATPHYS KOLKATA VII
Lepton asymmetry in the primordial gravitational wave spectrum
Effects of neutrino free streaming is evaluated on the primordial spectrum of
gravitational radiation taking both neutrino chemical potential and masses into
account. The former or the lepton asymmetry induces two competitive effects,
namely, to increase anisotropic pressure, which damps the gravitational wave
more, and to delay the matter-radiation equality time, which reduces the
damping. The latter effect is more prominent and a large lepton asymmetry would
reduce the damping. We may thereby be able to measure the magnitude of lepton
asymmetry from the primordial gravitational wave spectrum.Comment: 14 pages, 5 figure
Constraints on Neutrino Masses from Weak Lensing
The weak lensing (WL) distortions of distant galaxy images are sensitive to
neutrino masses by probing the suppression effect on clustering strengths of
total matter in large-scale structure. We use the latest measurement of WL
correlations, the CFHTLS data, to explore constraints on neutrino masses. We
find that, while the WL data alone cannot place a stringent limit on neutrino
masses due to parameter degeneracies, the constraint can be significantly
improved when combined with other cosmological probes, the WMAP 5-year (WMAP5)
data and the distance measurements of type-Ia supernovae (SNe) and baryon
acoustic oscillations (BAO). The upper bounds on the sum of neutrino masses are
m_tot = 1.1, 0.76 and 0.54 eV (95% CL) for WL+WMAP5, WMAP5+SNe+BAO, and
WL+WMAP5+SNe+BAO, respectively, assuming a flat LCDM model with finite-mass
neutrinos. In deriving these constraints, our analysis includes the
non-Gaussian covariances of the WL correlation functions to properly take into
account significant correlations between different angles.Comment: 16 pages, 10 figures. References added, accepted for publication in
PR
Precise Estimation of Cosmological Parameters Using a More Accurate Likelihood Function
The estimation of cosmological parameters from a given data set requires a
construction of a likelihood function which, in general, has a complicated
functional form. We adopt a Gaussian copula and constructed a copula likelihood
function for the convergence power spectrum from a weak lensing survey. We show
that the parameter estimation based on the Gaussian likelihood erroneously
introduces a systematic shift in the confidence region, in particular for a
parameter of the dark energy equation of state w. Thus, the copula likelihood
should be used in future cosmological observations.Comment: 5 pages, 3 figures. Maches version published by the Physical Review
Letter
Cosmic microwave background bispectrum of tensor passive modes induced from primordial magnetic fields
If the seed magnetic fields exist in the early Universe, tensor components of
their anisotropic stresses are not compensated prior to neutrino decoupling and
the tensor metric perturbations generated from them survive passively.
Consequently, due to the decay of these metric perturbations after
recombination, the so-called integrated Sachs-Wolfe effect, the large-scale
fluctuations of CMB radiation are significantly boosted. This kind of CMB
anisotropy is called the "tensor passive mode." Because these fluctuations
deviate largely from the Gaussian statistics due to the quadratic dependence on
the strength of the Gaussian magnetic field, not only the power spectrum but
also the higher-order correlations have reasonable signals. With these motives,
we compute the CMB bispectrum induced by this mode. When the magnetic spectrum
obeys a nearly scale-invariant shape, we obtain an estimation of a typical
value of the normalized reduced bispectrum as depending on the energy scale of the magnetic field
production from GeV to GeV. Here, is the
strength of the primordial magnetic field smoothed on . From the
above estimation and the current observational constraint on the primordial
non-Gaussianity, we get a rough constraint on the magnetic field strength as
.Comment: 5 pages, 2 figures. Accepted for publication in PR
Dynamics of radiating braneworlds
If the observable universe is a braneworld of Randall-Sundrum type, then
particle interactions at high energies will produce 5-dimensional gravitons
that escape into the bulk. As a result, the Weyl energy density on the brane
does not behave like radiation in the early universe, but does so only later,
in the low energy regime. Recently a simple model was proposed to describe this
modification of the Randall-Sundrum cosmology. We investigate the dynamics of
this model, and find the exact solution of the field equations. We use a
dynamical systems approach to analyze global features of the phase space of
solutions.Comment: error in figures corrected, reference adde
Phase transitions driven by L\'evy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations
Phase transitions and effects of external noise on many body systems are one
of the main topics in physics. In mean field coupled nonlinear dynamical
stochastic systems driven by Brownian noise, various types of phase transitions
including nonequilibrium ones may appear. A Brownian motion is a special case
of L\'evy motion and the stochastic process based on the latter is an
alternative choice for studying cooperative phenomena in various fields.
Recently, fractional Fokker-Planck equations associated with L\'evy noise have
attracted much attention and behaviors of systems with double-well potential
subjected to L\'evy noise have been studied intensively. However, most of such
studies have resorted to numerical computation. We construct an {\it
analytically solvable model} to study the occurrence of phase transitions
driven by L\'evy stable noise.Comment: submitted to EP
Effects of a primordial magnetic field with log-normal distribution on the cosmic microwave background
We study the effect of primordial magnetic fields (PMFs) on the anisotropies
of the cosmic microwave background (CMB). We assume the spectrum of PMFs is
described by log-normal distribution which has a characteristic scale, rather
than power-law spectrum. This scale is expected to reflect the generation
mechanisms and our analysis is complementary to previous studies with power-law
spectrum. We calculate power spectra of energy density and Lorentz force of the
log-normal PMFs, and then calculate CMB temperature and polarization angular
power spectra from scalar, vector, and tensor modes of perturbations generated
from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang,
and ACBAR data sets, we find that the current CMB data set places the strongest
constraint at Mpc with the upper limit
nG.Comment: 14 pages, 6 figure
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