6,669 research outputs found
Five-dimensional metric gravity and the accelerated universe
The metric theories of gravity are generalized to five-dimensional
spacetimes. By assuming a hypersurface-orthogonal Killing vector field
representing the compact fifth dimension, the five-dimensional theories are
reduced to their four-dimensional formalism. Then we study the cosmology of a
special class of models in a spatially flat FRW spacetime. It
is shown that the parameter can be constrained to a certain range by the
current observed deceleration parameter, and its lower bound corresponds to the
Kaluza-Klein theory. It turns out that both expansion and contraction of the
extra dimension may prescribe the smooth transition from the deceleration era
to the acceleration era in the recent past as well as an accelerated scenario
for the present universe. Hence five-dimensional gravity can naturally
account for the present accelerated expansion of the universe. Moreover, the
models predict a transition from acceleration to deceleration in the future,
followed by a cosmic recollapse within finite time. This differs from the
prediction of the five-dimensional Brans-Dicke theory but is in consistent with
a recent prediction based on loop quantum cosmology.Comment: 14 pages, 9 figures; Version published in PR
Dimension reduction and estimation in the secondary analysis of case-control studies
© 2018, Institute of Mathematical Statistics. All rights reserved. Studying the relationship between covariates based on retrospective data is the main purpose of secondary analysis, an area of increasing interest. We examine the secondary analysis problem when multiple covariates are available, while only a regression mean model is specified. Despite the completely parametric modeling of the regression mean function, the case-control nature of the data requires special treatment and semiparametric efficient estimation generates various nonparametric estimation problems with multivariate covariates. We devise a dimension reduction approach that fits with the specified primary and secondary models in the original problem setting, and use reweighting to adjust for the case-control nature of the data, even when the disease rate in the source population is unknown. The resulting estimator is both locally efficient and robust against the misspecification of the regression error distribution, which can be heteroscedastic as well as non-Gaussian. We demonstrate the advantage of our method over several existing methods, both analytically and numerically
A three-by-three matrix spectral problem for AKNS hierarchy and its binary Nonlinearization
A three-by-three matrix spectral problem for AKNS soliton hierarchy is
proposed and the corresponding Bargmann symmetry constraint involved in Lax
pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax
systems possess classical Hamiltonian structures, in which the nonlinearized
spatial system is intimately related to stationary AKNS flows. These
nonlinearized Lax systems also lead to a sort of involutive solutions to each
AKNS soliton equation.Comment: 21pages, in Late
Estimation and inference of error-prone covariate effect in the presence of confounding variables
© 2017, Institute of Mathematical Statistics. All rights reserved. We introduce a general single index semiparametric measurement error model for the case that the main covariate of interest is measured with error and modeled parametrically, and where there are many other variables also important to the modeling. We propose a semiparametric bias-correction approach to estimate the effect of the covariate of interest. The resultant estimators are shown to be root-n consistent, asymptotically normal and locally efficient. Comprehensive simulations and an analysis of an empirical data set are performed to demonstrate the finite sample performance and the bias reduction of the locally efficient estimators
Constraining Perturbative Early Dark Energy with Current Observations
In this work, we study a class of early dark energy (EDE) models, in which,
unlike in standard DE models, a substantial amount of DE exists in the
matter-dominated era, self-consistently including DE perturbations. Our
analysis shows that, marginalizing over the non DE parameters such as , current CMB observations alone can constrain the scale factor of
transition from early DE to late time DE to and width of
transition to . The equation of state at present is somewhat
weakly constrained to , if we allow km/s/Mpc. Taken
together with other observations, such as supernovae, HST, and SDSS LRGs, the
constraints are tighter-- .
The evolution of the equation of state for EDE models is thus close to
CDM at low redshifts. Incorrectly assuming DE perturbations to be
negligible leads to different constraints on the equation of state parameters,
thus highlighting the necessity of self-consistently including DE perturbations
in the analysis. If we allow the spatial curvature to be a free parameter, then
the constraints are relaxed to with for CMB+other observations. For
perturbed EDE models, the lower limit on () is much lower than that in CDM (), thus
raising the interesting possibility of discriminating EDE from CDM
using future observations such as halo mass functions or the Sunyaev-Zeldovich
power spectrum.Comment: 12 pages, 5 figures, references updated, accepted for publication in
Ap
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