Generalization of a theorem of Gonchar

Let $X, Y$ be two complex manifolds, let $D\subset X,$ $G\subset Y$ be two nonempty open sets, let $A$ (resp. $B$) be an open subset of $\partial D$ (resp. $\partial G$), and let $W$ be the 2-fold cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ Under a geometric condition on the boundary sets $A$ and $B,$ we show that every function locally bounded, separately continuous on $W,$ continuous on $A\times B,$ and separately holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a function continuous on a "domain of holomorphy" $\hat{W}$ and holomorphic on the interior of $\hat{W}.$Comment: 14 pages, to appear in Arkiv for Matemati

Cosmological Parameters Degeneracies and Non-Gaussian Halo Bias

We study the impact of the cosmological parameters uncertainties on the measurements of primordial non-Gaussianity through the large-scale non-Gaussian halo bias effect. While this is not expected to be an issue for the standard LCDM model, it may not be the case for more general models that modify the large-scale shape of the power spectrum. We consider the so-called local non-Gaussianity model and forecasts from planned surveys, alone and combined with a Planck CMB prior. In particular, we consider EUCLID- and LSST-like surveys and forecast the correlations among $f_{\rm NL}$ and the running of the spectral index $\alpha_s$, the dark energy equation of state $w$, the effective sound speed of dark energy perturbations $c^2_s$, the total mass of massive neutrinos $M_\nu=\sum m_\nu$, and the number of extra relativistic degrees of freedom $N_\nu^{rel}$. Neglecting CMB information on $f_{\rm NL}$ and scales $k > 0.03 h$/Mpc, we find that, if $N_\nu^{\rm rel}$ is assumed to be known, the uncertainty on cosmological parameters increases the error on $f_{\rm NL}$ by 10 to 30% depending on the survey. Thus the $f_{\rm NL}$ constraint is remarkable robust to cosmological model uncertainties. On the other hand, if $N_\nu^{\rm rel}$ is simultaneously constrained from the data, the $f_{\rm NL}$ error increases by $\sim 80$. Finally, future surveys which provide a large sample of galaxies or galaxy clusters over a volume comparable to the Hubble volume can measure primordial non-Gaussianity of the local form with a marginalized 1--$\sigma$ error of the order $\Delta f_{\rm NL} \sim 2-5$, after combination with CMB priors for the remaining cosmological parameters. These results are competitive with CMB bispectrum constraints achievable with an ideal CMB experiment.Comment: 17 pages, 1 figure added, typos corrected, comments added, matches the published versio

Direct and Indirect Detection of Dark Matter in D6 Flavor Symmetric Model

We study a fermionic dark matter in a non-supersymmetric extension of the standard model with a family symmetry based on D6xZ2xZ2. In our model, the final state of the dark matter annihilation is determined to be e+ e- by the flavor symmetry, which is consistent with the PAMELA result. At first, we show that our dark matter mass should be within the range of 230 GeV - 750 GeV in the WMAP analysis combined with mu to e gamma constraint. Moreover we simultaneously explain the experiments of direct and indirect detection, by simply adding a gauge and D6 singlet real scalar field. In the direct detection experiments, we show that the lighter dark matter mass ~ 230 GeV and the lighter standard model Higgs boson ~ 115 GeV is in favor of the observed bounds reported by CDMS II and XENON100. In the indirect detection experiments, we explain the positron excess reported by PAMELA through the Breit-Wigner enhancement mechanism. We also show that our model is consistent with no antiproton excess suggested by PAMELA.Comment: 20 pages, 9 figures, 2 tables, accepted version for publication in European Physical Journal

Some FRW Models of Accelerating Universe with Dark Energy

The paper deals with a spatially homogeneous and isotropic FRW space-time filled with perfect fluid and dark energy components. The two sources are assumed to interact minimally, and therefore their energy momentum tensors are conserved separately. A special law of variation for the Hubble parameter proposed by Berman (1983) has been utilized to solve the field equations. The Berman's law yields two explicit forms of the scale factor governing the FRW space-time and constant values of deceleration parameter. The role of dark energy with variable equation of state parameter has been studied in detail in the evolution of FRW universe. It has been found that dark energy dominates the universe at the present epoch, which is consistent with the observations. The physical behavior of the universe is discussed in detail.Comment: 10 pages, 5 figure

Constraints on the SZ Power Spectrum on Degree Angular Scales in WMAP Data

The Sunyaev-Zel'dovich (SZ) effect has a distinct spectral signature that allows its separation from fluctuations in the cosmic microwave background (CMB) and foregrounds. Using CMB anisotropies measured in Wilkinson Microwave Anisotropy Probe's five-year maps, we constrain the SZ fluctuations at large, degree angular scales corresponding to multipoles in the range from 10 to 400. We provide upper bounds on SZ fluctuations at multipoles greater than 50, and find evidence for a hemispherically asymmetric signal at ten degrees angular scales. The amplitude of the detected signal cannot be easily explained with the allowed number density and temperature of electrons in the Galactic halo. We have failed to explain the excess signal as a residual from known Galactic foregrounds or instrumental uncertainties such as 1/f-noise.Comment: 14 pages, 3 figures, 2 tables. Simple typos fixe

Limits on decaying dark energy density models from the CMB temperature-redshift relation

The nature of the dark energy is still a mystery and several models have been proposed to explain it. Here we consider a phenomenological model for dark energy decay into photons and particles as proposed by Lima (J. Lima, Phys. Rev. D 54, 2571 (1996)). He studied the thermodynamic aspects of decaying dark energy models in particular in the case of a continuous photon creation and/or disruption. Following his approach, we derive a temperature redshift relation for the CMB which depends on the effective equation of state $w_{eff}$ and on the "adiabatic index" $\gamma$. Comparing our relation with the data on the CMB temperature as a function of the redshift obtained from Sunyaev-Zel'dovich observations and at higher redshift from quasar absorption line spectra, we find $w_{eff}=-0.97 \pm 0.034$, adopting for the adiabatic index $\gamma=4/3$, in good agreement with current estimates and still compatible with $w_{eff}=-1$, implying that the dark energy content being constant in time.Comment: 8 pages, 1 figur

Reconstruction of the Dark Energy equation of state

One of the main challenges of modern cosmology is to investigate the nature of dark energy in our Universe. The properties of such a component are normally summarised as a perfect fluid with a (potentially) time-dependent equation-of-state parameter $w(z)$. We investigate the evolution of this parameter with redshift by performing a Bayesian analysis of current cosmological observations. We model the temporal evolution as piecewise linear in redshift between `nodes', whose $w$-values and redshifts are allowed to vary. The optimal number of nodes is chosen by the Bayesian evidence. In this way, we can both determine the complexity supported by current data and locate any features present in $w(z)$. We compare this node-based reconstruction with some previously well-studied parameterisations: the Chevallier-Polarski-Linder (CPL), the Jassal-Bagla-Padmanabhan (JBP) and the Felice-Nesseris-Tsujikawa (FNT). By comparing the Bayesian evidence for all of these models we find an indication towards possible time-dependence in the dark energy equation-of-state. It is also worth noting that the CPL and JBP models are strongly disfavoured, whilst the FNT is just significantly disfavoured, when compared to a simple cosmological constant $w=-1$. We find that our node-based reconstruction model is slightly disfavoured with respect to the $\Lambda$CDM model.Comment: 17 pages, 5 figures, minor correction

Large Scale Pressure Fluctuations and Sunyaev-Zel'dovich Effect

The Sunyaev-Zel'dovich (SZ) effect associated with pressure fluctuations of the large scale structure gas distribution will be probed with current and upcoming wide-field small angular scale cosmic microwave background experiments. We study the generation of pressure fluctuations by baryons which are present in virialized dark matter halos and by baryons present in small overdensities. For collapsed halos, assuming the gas distribution is in hydrostatic equilibrium with matter density distribution, we predict the pressure power spectrum and bispectrum associated with the large scale structure gas distribution by extending the dark matter halo approach which describes the density field in terms of correlations between and within halos. The projected pressure power spectrum allows a determination of the resulting SZ power spectrum due to virialized structures. The unshocked photoionized baryons present in smaller overdensities trace the Jeans-scale smoothed dark matter distribution. They provide a lower limit to the SZ effect due to large scale structure in the absence of massive collapsed halos. We extend our calculations to discuss higher order statistics, such as bispectrum and skewness in SZ data. The SZ-weak lensing cross-correlation is suggested as a probe of correlations between dark matter and baryon density fields, while the probability distribution functions of peak statistics of SZ halos in wide field CMB data can be used as a probe of cosmology and non-Gaussian evolution of large scale structure pressure fluctuations.Comment: 16 pages, 9 figures; Revised with expanded discussions. Phys. Rev. D. (in press

Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0

In this paper, instead of invoking Dark Energy, we try and fit various cosmological observations with a large Gpc scale under-dense region (Void) which is modeled by a Lemaitre-Tolman-Bondi metric that at large distances becomes a homogeneous FLRW metric. We improve on previous analyses by allowing for nonzero overall curvature, accurately computing the distance to the last-scattering surface and the observed scale of the Baryon Acoustic peaks, and investigating important effects that could arise from having nontrivial Void density profiles. We mainly focus on the WMAP 7-yr data (TT and TE), Supernova data (SDSS SN), Hubble constant measurements (HST) and Baryon Acoustic Oscillation data (SDSS and LRG). We find that the inclusion of a nonzero overall curvature drastically improves the goodness of fit of the Void model, bringing it very close to that of a homogeneous universe containing Dark Energy, while by varying the profile one can increase the value of the local Hubble parameter which has been a challenge for these models. We also try to gauge how well our model can fit the large-scale-structure data, but a comprehensive analysis will require the knowledge of perturbations on LTB metrics. The model is consistent with the CMB dipole if the observer is about 15 Mpc off the centre of the Void. Remarkably, such an off-center position may be able to account for the recent anomalous measurements of a large bulk flow from kSZ data. Finally we provide several analytical approximations in different regimes for the LTB metric, and a numerical module for CosmoMC, thus allowing for a MCMC exploration of the full parameter space.Comment: 70 pages, 12 figures, matches version accepted for publication in JCAP. References added, numerical values in tables changed due to minor bug, conclusions unaltered. Numerical module available at http://web.physik.rwth-aachen.de/download/valkenburg

Chameleonic Generalized Brans--Dicke model and late-time acceleration

In this paper we consider Chameleonic Generalized Brans--Dicke Cosmology in the framework of FRW universes. The bouncing solution and phantom crossing is investigated for the model. Two independent cosmological tests: Cosmological Redshift Drift (CRD) and distance modulus are applied to test the model with the observation.Comment: 20 pages, 15 figures, to be published in Astrophys. Space Sci. (2011