Hawking radiation of Dirac fields in the (2+1)-dimensional black hole space-time.
By calculating the response function, we study the Hawking radiation of massless Dirac fields in the (2+1)-dimensional black hole geometry. We find that the response function has Planck distributions, with the temperature that agrees with the previous results obtained for the scalar field cases. We also find the Green's functions in (2+1)-dimensional Einstein static universe and anti de-Sitter space.

title: Probing modifications of general relativity using current cosmological observations
abstract: We test general relativity (GR) using current cosmological data: the CMB from WMAP5 [E. Komatsu et al. (WMAP Collaboration),  (2009)], the integrated Sachs-Wolfe (ISW) effect from the cross correlation of the CMB with six galaxy catalogs [T. Giannantonio et al.,  (2008)], a compilation of supernovae (SNe) type Ia including the latest Sloan Digital Sky Survey SNe [R. Kessler et al.,  (2009).], and part of the weak lensing (WL) data from the Canada-Franco-Hawaii Telescope Legacy Survey [L. Fu et al.,  (2008); M. Kilbinger et al.,  (2009).] that probe linear and mildly nonlinear scales. We first test a model in which the effective Newtonian constant μ and the ratio of the two gravitational potentials, η, transit from the GR value to another constant at late times; in this case, we find that GR is fully consistent with the combined data. The strongest constraint comes from the ISW effect which would arise from this gravitational transition; the observed ISW signal imposes a tight constraint on a combination of μ and η that characterizes the lensing potential. Next, we consider four pixels in time and space for each function μ and η, and perform a principal component analysis, finding that seven of the resulting eight eigenmodes are consistent with GR within the errors. Only one eigenmode shows a 2σ deviation from the GR prediction, which is likely to be due to a systematic effect. However, the detection of such a deviation demonstrates the power of our time- and scale-dependent principal component analysis methodology when combining observations of structure formation and expansion history to test GR.

title: Conformal invariance of curvature perturbation
abstract: We show that in the single component situation all perturbation variables in the comoving gauge are conformally invariant to all perturbation orders. Generally we identify a special time slicing, the uniform-conformal transformation slicing, where all perturbations are again conformally invariant to all perturbation orders. We apply this result to the δN formalism, and show its conformal invariance.

title: Distance-redshift and growth-redshift relations as two windows on acceleration and gravitation : Dark energy or new gravity?
abstract: Small distortions in the observed shapes of distant galaxies, a cosmic shear due to gravitational lensing, can be used to simultaneously determine the distance-redshift relation, $r(z)$, and the density contrast growth factor, $g(z)$. Both of these functions are sensitive probes of the acceleration. Their simultaneous determination allows for a consistency test and provides sensitivity to physics beyond the standard dark energy paradigm.

title: Chasing unbiased spectra of the Universe
abstract: The cosmological power spectrum of the coherent matter flow is measured exploiting an improved prescription for the apparent anisotropic clustering pattern in redshift space. New statistical analysis is presented to provide an optimal observational platform to link the improved redshift distortion theoretical model to future real datasets. The statistical power as well as robustness of our method are tested against 60 realizations of 8 Gpc/h^3 dark matter simulation maps mocking the precision level of upcoming wide--deep surveys. We showed that we can accurately extract the velocity power spectrum up to quasi linear scales of k~0.1 h/Mpc at z = 0.35 and up to k~0.15 h/Mpc at higher redshifts within a couple of percentage precision level. Our understanding of redshift space distortion is proved to be appropriate for precision cosmology, and our statistical method will guide us to righteous path to meet the real world.

title: Complementarity of weak lensing and peculiar velocity measurements in testing general relativity
abstract: We explore the complementarity of weak lensing and galaxy peculiar velocity measurements to better constrain modifications to General Relativity. We find no evidence for deviations from General Relativity on cosmological scales from a combination of peculiar velocity measurements (for Luminous Red Galaxies in the Sloan Digital Sky Survey) with weak lensing measurements (from the Canadian France Hawaii Telescope Legacy Survey). We provide a Fisher error forecast for a Euclid-like space-based survey including both lensing and peculiar velocity measurements and show that the expected constraints on modified gravity will be at least an order of magnitude better than with present data, i.e. we will obtain {approx_equal}5% errors on the modified gravity parametrization described here. We also present a model-independent method for constraining modified gravity parameters using tomographic peculiar velocity information, and apply this methodology to the present data set.

title: Coulomb instability in hot nuclei with Skyrme interaction.
abstract: Coulomb instability in hot nuclei is discussed, using the Skyrme effective nucleon-nucleon interactions and a mean-field approach based on a finite-temperature real-time Green's-function method. In the calculation, full degeneracy and symmetry corrections are included. It is found that the above precise treatment of degeneracy and symmetry corrections is necessary in the lower-temperature and higher-density region or for larger asymmetry. The calculated limiting temperatures are quite different for different sets of Skyrme effective interactions, which may be used as a sensitive test of the various Skyrme interactions to see which one can best describe the finite-temperature properties of nuclear matter. It is also found that the limiting temperature ${\mathit{T}}_{\mathrm{lim}}$ is approximately proportional to the critical temperature ${\mathit{T}}_{\mathit{C}}$, when the results for various Skyrme interactions are compared.