We investigate the interacting dark energy models by using the diagnostics of statefinder hierarchy and growth rate of structure. We wish to explore the deviations from $Lambda$CDM and to differentiate possible degeneracies in the interacting dark en
ergy models with the geometrical and structure growth diagnostics. We consider two interacting forms for the models, i.e., $Q_1=beta Hrho_c$ and $Q_2=beta Hrho_{de}$, with $beta$ being the dimensionless coupling parameter. Our focus is the I$Lambda$CDM model that is a one-parameter extension to $Lambda$CDM by considering a direct coupling between the vacuum energy ($Lambda$) and cold dark matter (CDM), with the only additional parameter $beta$. But we begin with a more general case by considering the I$w$CDM model in which dark energy has a constant $w$ (equation-of-state parameter). For calculating the growth rate of structure, we employ the parametrized post-Friedmann theoretical framework for interacting dark energy to numerically obtain the $epsilon(z)$ values for the models. We show that in both geometrical and structural diagnostics the impact of $w$ is much stronger than that of $beta$ in the I$w$CDM model. We thus wish to have a closer look at the I$Lambda$CDM model by combining the geometrical and structural diagnostics. We find that the evolutionary trajectories in the $S^{(1)}_3$--$epsilon$ plane exhibit distinctive features and the departures from $Lambda$CDM could be well evaluated, theoretically, indicating that the composite null diagnostic ${S^{(1)}_3, epsilon}$ is a promising tool for investigating the interacting dark energy models.
The model of holographic dark energy (HDE) with massive neutrinos and/or dark radiation is investigated in detail. The background and perturbation evolutions in the HDE model are calculated. We employ the PPF approach to overcome the gravity instabil
ity difficulty (perturbation divergence of dark energy) led by the equation-of-state parameter $w$ evolving across the phantom divide $w=-1$ in the HDE model with $c<1$. We thus derive the evolutions of density perturbations of various components and metric fluctuations in the HDE model. The impacts of massive neutrino and dark radiation on the CMB anisotropy power spectrum and the matter power spectrum in the HDE scenario are discussed. Furthermore, we constrain the models of HDE with massive neutrinos and/or dark radiation by using the latest measurements of expansion history and growth of structure, including the Planck CMB temperature data, the baryon acoustic oscillation data, the JLA supernova data, the Hubble constant direct measurement, the cosmic shear data of weak lensing, the Planck CMB lensing data, and the redshift space distortions data. We find that $sum m_ u<0.186$ eV (95% CL) and $N_{rm eff}=3.75^{+0.28}_{-0.32}$ in the HDE model from the constraints of these data.
In this paper, we constrain the dimensionless Compton wavelength parameter $B_0$ of $f(R)$ gravity as well as the mass of sterile neutrino by using the cosmic microwave background observations, the baryon acoustic oscillation surveys, and the linear
growth rate measurements. Since both the $f(R)$ model and the sterile neutrino generally predict scale-dependent growth rates, we utilize the growth rate data measured in different wavenumber bins with the theoretical growth rate approximatively scale-independent in each bin. The employed growth rate data come from the peculiar velocity measurements at $z=0$ in five wavenumber bins, and the redshift space distortions measurements at $z=0.25$ and $z=0.37$ in one wavenumber bin. By constraining the $f(R)$ model alone, we get a tight 95% upper limit of $log_{10}B_0<-4.1$. This result is slightly weakened to $log_{10}B_0<-3.8$ (at 2$sigma$ level) once we simultaneously constrain the $f(R)$ model and the sterile neutrino mass, due to the degeneracy between the parameters of the two. For the massive sterile neutrino parameters, we get the effective sterile neutrino mass $m_{ u,{rm{sterile}}}^{rm{eff}}<0.62$ eV (2$sigma$) and the effective number of relativistic species $N_{rm eff}<3.90$ (2$sigma$) in the $f(R)$ model. As a comparison, we also obtain $m_{ u,{rm{sterile}}}^{rm{eff}}<0.56$ eV (2$sigma$) and $N_{rm eff}<3.92$ (2$sigma$) in the standard $Lambda$CDM model.
Experimental measurements clearly reveal the presence of bulk superconductivity in the CsPbxBi4-xTe6 (0.3=<x=<1.0) materials, i.e. the first member of the thermoelectric series of Cs[PbmBi3Te5+m], these materials have the layered orthorhombic structu
re containing infinite anionic [PbBi3Te6]- slabs separated with Cs+ cations. Temperature dependences of electrical resistivity, magnetic susceptibility, and specific heat have consistently demonstrated that the superconducting transition in CsPb0.3Bi3.7Te6 occurs at Tc=3.1K, with a superconducting volume fraction close to 100% at 1.8 K. Structural study using aberration-corrected STEM/TEM reveals a rich variety of microstructural phenomena in correlation with the Pb-ordering and chemical inhomogeneity. The superconducting material CsPb0.3Bi3.7Te6 with the highest Tc shows a clear ordered structure with a modulation wave vector of q=a*/2+ c*/1.35 on the a-c plane. Our study evidently demonstrates that superconductivity deriving upon doping of narrow-gap semiconductor is a viable approach for exploration of novel superconductors.
The origin of ultra-compact dwarfs (UCDs)--objects larger and more massive than typical globular clusters (GCs), but more compact than typical dwarf galaxies--has been hotly debated in the 15 years since their discovery. Even whether UCDs should be c
onsidered galactic in origin, or simply the most extreme GCs, is not yet settled. We present the dynamical properties of 97 spectroscopically confirmed UCDs (rh >~10 pc) and 911 GCs associated with central cD galaxy of the Virgo cluster, M87. Our UCDs, of which 89% have M_star > ~2X10^6 M_sun and 92% are as blue as the classic blue GCs, nearly triple the sample of previous confirmed Virgo UCDs, providing by far the best opportunity for studying the global dynamics of a UCD system. We found that (1) UCDs have a surface number density profile that is shallower than that of the blue GCs in the inner ~ 70 kpc and as steep as that of the red GCs at larger radii; (2) UCDs exhibit a significantly stronger rotation than the GCs, and the blue GCs seem to have a velocity field that is more consistent with that of the surrounding dwarf ellipticals than with that of UCDs; (3) UCDs have a radially increasing orbital anisotropy profile, and are tangentially-biased at radii < ~ 40 kpc and radially-biased further out. In contrast, the blue GCs become more tangentially-biased at larger radii beyond ~ 40 kpc; (4) GCs with M_star > 2X10^6 M_sun have rotational properties indistinguishable from the less massive ones, suggesting that it is the size, instead of mass, that differentiates UCDs from GCs as kinematically distinct populations. We conclude that most UCDs in M87 are not consistent with being merely the most luminous and extended examples of otherwise normal GCs. The radially-biased orbital structure of UCDs at large radii is in general agreement with the tidally threshed dwarf galaxy scenario.
