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We study Einstein-Gauss-Bonnet gravity coupled to a bumblebee field which leads to a spontaneous Lorentz symmetry breaking in the gravitational sector. We obtain an exact black hole solution and a cosmological solution in four dimensional spacetime by a regularization scheme. We also obtain a Schwarzschild-like bumblebee black hole solution in $D$-dimensional spacetime. We find that the bumblebee field doesn't affect the locations of the black hole horizon, but only affects the gravitational potential. That is, its gravitational potential has a minimum value(negative) in the black hole interior and has a positive value $1+\ell$ at short distance $r\rightarrow0$. If the constant $\ell$ is large enough, then this kind of black hole is practically free from the singularity problem. The thermodynamics and phase transition are also studied. In a cosmological context, it is interesting that the Gauss-Bonnet term has no effect on the conservation of energy equation. A late-time expansion of de Sitter universe can be replicated in an empty space. The Gauss-Bonnet term and the bumblebee field can both actually act as a form of dark energy., 18 pages, four figures, accepted by Nucl. Phys. B

In this work, using the Gaussian process, we explore the potentiality of future gravitational wave (GW) measurements to probe cosmic opacity at high redshifts through comparing its opacity-free luminosity distance (LD) with the opacity-dependent one from the combination of Type Ia supernovae (SNIa) and gamma-ray bursts (GRBs). The GW data, SNIa and GRB data are simulated from the measurements of the future Einstein Telescope, the actual Pantheon compilation and the latest observation of GRBs compiled by L. Amati {\it et al}, respectively. A nonparametric method is proposed to probe the spatial homogeneity of cosmic transparency at high redshift by comparing the LD reconstructed from the GW data with that reconstructed from the Pantheon and GRB data. In addition, the cosmic opacity is tested by using the parametrization for the optical depth, and the results show that the constraints on cosmic opacity are more stringent than the previous ones. It shows that the future GW measurements may be used as an important tool to probe the cosmic opacity in the high redshift region., 21pages, 3 figures accepted by EPJC. arXiv admin note: text overlap with arXiv:1912.02327

A validation of the cosmic distance-duality relation (CDDR) is crucial because any observational departure from it could be a signal of new physics. In this work, we explore the potentialities of luminosity distance data from the gravitational wave (GW) standard sirens of future Einstein Telescope (ET) to test the CDDR. The angular diameter distance data are used from the galaxy clusters samples and the baryon acoustic oscillation (BAO) measurements. The basic advantage of GW measurements substituting for the observations from the type Ia supernovae (SNIa) is that the luminosity distance from it is insensitive to the non-conservation of the number of photons. By simulating 550 and 1000 data points of future GW measurements in the low redshift range $0, Comment: Submitted to PRD 17pages,3figs

In this work, using the Gaussian Process, we explore the potentiality of future gravitational wave (GW) measurement to probe cosmic opacity through comparing its opacity-free luminosity distance (LD) with the opacity-dependent one from type Ia supernovae (SNIa). GW data points are simulated from the third generation Einstein Telescope, and SNIa data are taken from the Joint Light Analysis (JLA) or Pantheon compilation. The advantages of using Gaussian Process are that one may match SNIa data with GW data at the same redshift and use all available data to probe cosmic opacity. We obtain that the error bar of the constraint on cosmic opacity can be reduced to $\sigma_{\epsilon}\sim 0.011$ and $0.006$ at $1\sigma$ confidence level (CL) for JLA and Pantheon respectively in a cosmological-independent way. Thus, the future GW measurements can give competitive results on the cosmic opacity test. Furthermore, we propose a method to probe the spatial homogeneity of the cosmic transparency through comparing the reconstructed LD from the mock GW with the reconstructed one from SNIa data in a flat $\Lambda$CDM with the Gaussian Process. The result shows that a transparent universe is favored at $1\sigma$ CL, although the best-fit value of cosmic opacity is redshift-dependent., Comment: 19pages, 3figures, accepted by PRD

In this paper, we perform a cosmological model-independent test of the cosmic distance-duality relation (CDDR) in terms of the ratio of angular diameter distance (ADD) $D=D_{\rm A}^{\rm sl}/D_{\rm A}^{\,\rm s}$ from strong gravitational lensing (SGL) and the ratio of luminosity distance (LD) $D^\ast=D_{\rm L}^{\,\rm l}/D_{\rm L}^{\,\rm s}$ obtained from the joint of type Ia supernovae (SNIa) Union2.1 compilation and the latest Gamma-Ray Bursts (GRBs) data, where the superscripts s and l correspond to the redshifts $z_{\,\rm s}$ and $z_{\,\rm l}$ at the source and lens from SGL samples. The purpose of combining GRB data with SNIa compilation is to test CDDR in a wider redshift range. The LD associated with the redshits of the observed ADD, is obtained through two cosmological model-independent methods, namely, method A: binning the SNIa+GRBs data, and method B: reconstructing the function of DL by combining the Crossing Statistic with the smoothing method. We find that CDDR is compatible with the observations at $1\sigma$ confidence level for the power law model which is assumed to describe the mass distribution of lensing systems with method B in a wider redshift range., Comment: 18pages and 5figures

In this paper, we study the growth index of matter density perturbations for the power law model in $f(T)$ gravity. Using the parametrization $\gamma(z)=\gamma_0+\gamma_1 {z\over 1+z}$ for the growth index, which approximates the real evolution of $\gamma(z)$ very well, and the observational data of the growth factor, we find that, at $1\sigma$ confidence level, the power law model in $f(T)$ gravity is consistent with the observations, since the obtained theoretical values of $\gamma_0$ and $\gamma_1$ are in the allowed region., Comment: 11 pages 4 figures

The growth of matter perturbations in the $f(R)$ model proposed by Starobinsky is studied in this paper. Three different parametric forms of the growth index are considered respectively and constraints on the model are obtained at both the $1\sigma$ and $2\sigma$ confidence levels, by using the current observational data for the growth factor. It is found, for all the three parametric forms of the growth index examined, that the Starobinsky model is consistent with the observations only at the $2\sigma$ confidence level., Comment: 15 pages, 5 figures

We study the linear growth of matter perturbations in the DGP model with the growth index $\gamma$ as a function of redshift. At the linear approximation: $\gamma(z)\approx\gamma_0+\gamma_0^\prime z $, we find that, for $0.2\leq\Omega_{m,0}\leq0.35$, $\gamma_0$ takes the value from 0.658 to 0.671, and $\gamma_0^\prime$ ranges from 0.035 to 0.042. With three low redshift observational data of the growth factor, we obtain the observational constraints on $\gamma_0$ and $\gamma_0'$ for the $\Lambda CDM$ and DGP models and find that the observations favor the $\Lambda CDM$ model but at the $1\sigma$ confidence level both the $\Lambda CDM$ and DGP models are consistent with the observations., Comment: 12 pages, 4 figuers, to appear in PLB

The unparticle has been suggested as a candidate of dark matter. We investigated the growth rate of the density perturbation for the unparticle dark matter in the flat Universe. First, we consider the model in which unparticle is the sole dark matter and find that the growth factor can be approximated well by $f=(1+3\omega_u)\Omega^{\gamma}_u$, where $\omega_u$ is the equation of state of unparticle. Our results show that the presence of $\omega_u$ modifies the behavior of the growth factor $f$. For the second model where unparticle co-exists with cold dark matter, the growth factor has a new approximation $f=(1+3\omega_u)\Omega^{\gamma}_u+\alpha \Omega_m$ and $\alpha $ is a function of $\omega_u$. Thus the growth factor of unparticle is quite different from that of usual dark matter. These information can help us know more about unparticle and the early evolution of the Universe., Comment: 6pages, 4 figures, accepted for publication in Eur. Phys. J. C

We study the dynamics of a phantom scalar field dark energy interacting with dark matter in loop quantum cosmology (LQC). Two kinds of coupling of the form $\alpha{\rho_m}{\dot\phi}$ (case I) and $3\beta H (\rho_\phi +\rho_m)$ (case II) between the phantom energy and dark matter are examined with the potential for the phantom field taken to be exponential. For both kinds of interactions, we find that the future singularity appearing in the standard FRW cosmology can be avoided by loop quantum gravity effects. In case II, if the phantom field is initially rolling down the potential, the loop quantum effect has no influence on the cosmic late time evolution and the universe will accelerate forever with a constant energy ratio between the dark energy and dark matter., Comment: 18 pages, 7 figures, PRD published version

We propose a parametrization for the growth index of the linear matter perturbations, $\gamma(z)=\gamma_0+\frac{z}{1+z}\gamma_1$. The growth factor of the perturbations parameterized as $\Omega_m^{\gamma}$ is analyzed for both the $w$CDM model and the DGP model with our proposed form for $\gamma$. We find that $\gamma_1$ is negative for the $w$CDM model but is positive for the DGP model. Thus it provides another signature to discriminate them. We demonstrate that $\Omega_m^{\gamma}$ with $\gamma$ taking our proposed form approximates the growth factor very well both at low and high redshfits for both kinds of models. In fact, the error is below 0.03% for the $\Lambda$CDM model and 0.18% for the DGP model for all redshifts when $\Omega_{m0}=0.27$. Therefore, our parametrization may be robustly used to constrain the growth index of different models with the observational data which include points for redshifts ranging from 0.15 to 3.8, thus providing discriminative signatures for different models., Comment: 14 pages, 6 figures; Added references