Non-minimal Derivative Coupling Scalar Field and Bulk Viscous Dark Energy

Inspired by thermodynamical dissipative phenomena, we consider bulk viscosity for dark fluid in a spatially flat two-component Universe. Our viscous dark energy model represents Phantom crossing avoiding Big-Rip singularity. We propose a non-minimal derivative coupling scalar field with zero potential leading to accelerated expansion of Universe in the framework of bulk viscous dark energy model. In this approach, coupling constant ($\kappa$) is related to viscosity coefficient ($\gamma$) and energy density of dark energy at the present time ($\Omega_{\rm DE}^0$). This coupling is bounded as $\kappa\in [-1/9H_0^2(1-\Omega_{\rm DE}^0), 0]$ and for $\gamma=0$ leads to $\kappa=0$. To perform robust analysis, we implement recent observational data sets including Joint Light-curve Analysis (JLA) for SNIa, Gamma Ray Bursts (GRBs) for most luminous astrophysical objects at high redshifts, Baryon Acoustic Oscillations (BAO) from different surveys, Hubble parameter from HST project, {\it Planck} data for CMB power spectrum and CMB Lensing. Joint analysis of JLA$+$GRBs$+$BAO$+$HST shows that $\Omega_{\rm DE}^0=0.696\pm 0.010$, $\gamma=0.1404\pm0.0014$ and $H_0=68.1\pm1.3$ at $1\sigma$ confidence interval. {\it Planck} TT observation provides $\gamma=0.32^{+0.31}_{-0.26}$ at $68\%$ confidence limit for viscosity coefficient. Tension in Hubble parameter is alleviated in this model. Cosmographic distance ratio indicates that current observed data prefer to increase bulk viscosity. Finally, the competition between Phantom and Quintessence behavior of viscous dark energy model can accommodate cosmological old objects reported as a sign of age crisis in $\Lambda$CDM model.Comment: 21 pages and 18 figures, some typos in equations fixe

Assessment of 48 Stock markets using adaptive multifractal approach

Stock market comovements are examined using cointegration, Granger causality tests and nonlinear approaches in context of mutual information and correlations. Underlying data sets are affected by non-stationarities and trends, we also apply AMF-DFA and AMF-DXA. We find only 170 pair of Stock markets cointegrated, and according to the Granger causality and mutual information, we realize that the strongest relations lies between emerging markets, and between emerging and frontier markets. According to scaling exponent given by AMF-DFA, $h(q=2)>1$, we find that all underlying data sets belong to non-stationary process. According to EMH, only 8 markets are classified in uncorrelated processes at $2\sigma$ confidence interval. 6 Stock markets belong to anti-correlated class and dominant part of markets has memory in corresponding daily index prices during January 1995 to February 2014. New-Zealand with $H=0.457\pm0.004$ and Jordan with $H=0.602\pm 0.006$ are far from EMH. The nature of cross-correlation exponents based on AMF-DXA is almost multifractal for all pair of Stock markets. The empirical relation, $H_{xy}\le [H_{xx}+H_{yy}]/2$, is confirmed. Mentioned relation for $q>0$ is also satisfied while for $q<0$ there is a deviation from this relation confirming behavior of markets for small fluctuations is affected by contribution of major pair. For larger fluctuations, the cross-correlation contains information from both local and global conditions. Width of singularity spectrum for auto-correlation and cross-correlation are $\Delta \alpha_{xx}\in [0.304,0.905]$ and $\Delta \alpha_{xy}\in [0.246,1.178]$, respectively. The wide range of singularity spectrum for cross-correlation confirms that the bilateral relation between Stock markets is more complex. The value of $\sigma_{DCCA}$ indicates that all pairs of stock market studied in this time interval belong to cross-correlated processes.Comment: 16 pages, 13 figures and 4 tables, major revision and match to published versio