9,514 research outputs found
Application of functional analysis to perturbation theory of differential equations
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point
Age problem in holographic dark energy
We study the age problem of the universe with the holographic DE model
introduced in [21], and test the model with some known old high redshift
objects (OHRO). The parameters of the model have been constrained using the
SNIa, CMB and BAO data set. We found that the age of the old quasar APM 08
279+5255 at z = 3.91 can be described by the model.Comment: 13 page
The Imprint of Gravitational Waves on the Cosmic Microwave Background
Long-wavelength gravitational waves can induce significant temperature
anisotropy in the cosmic microwave background. Distinguishing this from
anisotropy induced by energy density fluctuations is critical for testing
inflationary cosmology and theories of large-scale structure formation. We
describe full radiative transport calculations of the two contributions and
show that they differ dramatically at angular scales below a few degrees. We
show how anisotropy experiments probing large- and small-angular scales can
combine to distinguish the imprint due to gravitational waves.Comment: 11 pages, Penn Preprint-UPR-
Primordial magnetic field and non-Gaussianity of the 1-year Wilkinson Microwave Anisotropy Probe (WMAP) data
Alfven turbulence caused by statistically isotropic and homogeneous
primordial magnetic field induces correlations in the cosmic microwave
background anisotropies. The correlations are specifically between spherical
harmonic modes a_{l-1,m} and a_{l+1,m}. In this paper we approach this issue
from phase analysis of the CMB maps derived from the WMAP data sets. Using
circular statistics and return phase mapping we examine phase correlation of
\Delta l=2 for the primordial non-Gaussianity caused by the Alfven turbulence
at the epoch of recombination. Our analyses show that such specific features
from the power-law Alfven turbulence do not contribute significantly in the
phases of the maps and could not be a source of primordial non-Gaussianity of
the CMB.Comment: 8 pages, 7 figures, ApJ accepted with minor changes and the
explanation on the whitened derived CMB map
Probing the Coupling between Dark Components of the Universe
We place observational constraints on a coupling between dark energy and dark
matter by using 71 Type Ia supernovae (SNe Ia) from the first year of the
five-year Supernova Legacy Survey (SNLS), the cosmic microwave background (CMB)
shift parameter from the three-year Wilkinson Microwave Anisotropy Probe
(WMAP), and the baryon acoustic oscillation (BAO) peak found in the Sloan
Digital Sky Survey (SDSS). The interactions we study are (i) constant coupling
delta and (ii) varying coupling delta(z) that depends on a redshift z, both of
which have simple parametrizations of the Hubble parameter to confront with
observational data. We find that the combination of the three databases
marginalized over a present dark energy density gives stringent constraints on
the coupling, -0.08 < delta < 0.03 (95% CL) in the constant coupling model and
-0.4 < delta_0 < 0.1 (95% CL) in the varying coupling model, where delta_0 is a
present value. The uncoupled LambdaCDM model (w_X = -1 and delta = 0) still
remains a good fit to the data, but the negative coupling (delta < 0) with the
equation of state of dark energy w_X < -1 is slightly favoured over the
LambdaCDM model.Comment: 9 pages, 7 figures, RevTeX, minor corrections, references added,
accepted for publication in Phys. Rev.
Future CMB Constraints on Early, Cold, or Stressed Dark Energy
We investigate future constraints on early dark energy (EDE) achievable by
the Planck and CMBPol experiments, including cosmic microwave background (CMB)
lensing. For the dark energy, we include the possibility of clustering through
a sound speed c_s^2 <1 (cold dark energy) and anisotropic stresses
parameterized with a viscosity parameter c_vis^2. We discuss the degeneracies
between cosmological parameters and EDE parameters. In particular we show that
the presence of anisotropic stresses in EDE models can substantially undermine
the determination of the EDE sound speed parameter c_s^2. The constraints on
EDE primordial energy density are however unaffected. We also calculate the
future CMB constraints on neutrino masses and find that they are weakened by a
factor of 2 when allowing for the presence of EDE, and highly biased if it is
incorrectly ignored.Comment: 12 pages, 19 figure
Cosmic Constraint to DGP Brane Model: Geometrical and Dynamical Perspectives
In this paper, the Dvali-Gabadadze-Porrati (DGP) brane model is confronted by
current cosmic observational data sets from geometrical and dynamical
perspectives. On the geometrical side, the recent released Union2 of type
Ia supernovae (SN Ia), the baryon acoustic oscillation (BAO) from Sloan Digital
Sky Survey and the Two Degree Galaxy Redshift Survey (transverse and radial to
line-of-sight data points), the cosmic microwave background (CMB) measurement
given by the seven-year Wilkinson Microwave Anisotropy Probe observations
(shift parameters , and redshift at the last scatter surface
), ages of high redshifts galaxies, i.e. the lookback time (LT) and the
high redshift Gamma Ray Bursts (GRBs) are used. On the dynamical side, data
points about the growth function (GF) of matter linear perturbations are used.
Using the same data sets combination, we also constrain the flat CDM
model as a comparison. The results show that current geometrical and dynamical
observational data sets much favor flat CDM model and the departure
from it is above () for spatially flat DGP model
with(without) SN systematic errors. The consistence of growth function data
points is checked in terms of relative departure of redshift-distance relation.Comment: 14 pages, 5 figures, 2 tables, accepted for publication in Physical
Review
Gravitational Lensing Effect on the Two-point Correlation of Hotspots in the Cosmic Microwave Background
We investigate the weak gravitational lensing effect due to the large-scale
structure of the universe on two-point correlations of local maxima ({\em
hotspots}) in the 2D sky map of the cosmic microwave background (CMB)
anisotropy. According to the Gaussian random statistics as most inflationary
scenarios predict, the hotspots are discretely distributed with some {\em
characteristic} angular separations on the last scattering surface owing to
oscillations of the CMB angular power spectrum.
The weak lensing then causes pairs of hotspots which are separated with the
characteristic scale to be observed with various separations. We found that the
lensing fairly smoothes the oscillatory features of the two-point correlation
function of hotspots. This indicates that the hotspots correlations can be a
new statistical tool for measuring shape and normalization of the power
spectrum of matter fluctuations from the lensing signatures.Comment: 6 pages, 2 figures; replaced with published versio
Constraints on a New Post-General Relativity Cosmological Parameter
A new cosmological variable is introduced which characterizes the degree of
departure from Einstein's General Relativity (GR) with a cosmological constant.
The new parameter, \varpi, is the cosmological analog of \gamma, the
parametrized post-Newtonian variable which measures the amount of spacetime
curvature per unit mass. In the cosmological context, \varpi measures the
difference between the Newtonian and longitudinal potentials in response to the
same matter sources, as occurs in certain scalar-tensor theories of gravity.
Equivalently, \varpi measures the scalar shear fluctuation in a dark energy
component. In the context of a "vanilla" LCDM background cosmology, a non-zero
\varpi signals a departure from GR or a fluctuating cosmological constant.
Using a phenomenological model for the time evolution \varpi=\varpi_0
\rho_{DE}/\rho_{M} which depends on the ratio of energy density in the
cosmological constant to the matter density at each epoch, it is shown that the
observed cosmic microwave background (CMB) temperature anisotropies limit the
overall normalization constant to be -0.4 < \varpi_0 < 0.1 at the 95%
confidence level. Existing measurements of the cross-correlations of the CMB
with large-scale structure further limit \varpi_0 > -0.2 at the 95% CL. In the
future, integrated Sachs-Wolfe and weak lensing measurements can more tightly
constrain \varpi_0, providing a valuable clue to the nature of dark energy and
the validity of GR.Comment: 9 pages, 7 figures; added reference
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