We propose a parametrization for the growth index of the linear matter perturbations, γ(z) = γ 0 + z 1+z γ 1 . The growth factor of the perturbations parameterized as Ω γ m is analyzed for both the wCDM model and the DGP model with our proposed form for γ. We find that γ 1 is negative for the wCDM model but is positive for the DGP model. Thus it provides another signature to discriminate them. We demonstrate that Ω γ m with γ 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 ΛCDM model and 0.18% for the DGP model for all redshifts when Ω 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.

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 αρ mφ (case I) and 3βH(ρ φ + ρ 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.

We study the linear growth of matter perturbations in the DGP model with the growth index γ as a function of redshift. At the linear approximation: γ(z) ≈ γ 0 + γ ′ 0 z, we find that, for 0.2 ≤ Ω m,0 ≤ 0.35, γ 0 takes the value from 0.658 to 0.671, and γ ′ 0 ranges from 0.035 to 0.042.With three low redshift observational data of the growth factor, we obtain the observational constraints on γ 0 and γ ′ 0 for the ΛCDM and DGP models and find that the observations favor the ΛCDM model but at the 1σ confidence level both the ΛCDM and DGP models are consistent with the observations. PACS numbers: 95.36.+x, 98.80.Es

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 1σ and 2σ 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 2σ confidence level.

We study the Brownian motion of a charged test particle driven by quantum electromagnetic fluctuations in the vacuum region near a non-dispersive and non-absorbing dielectric half-space and calculate the mean squared fluctuations in the velocity of the test particle.Our results show that a nonzero susceptibility of the dielectrics has its imprints on the velocity dispersions of the test particles. The most noteworthy feature in sharp contrast to the case of an idealized perfectly conducting interface is that the velocity dispersions in the parallel directions are no longer negative and does not die off in time, suggesting that the potentially problematic negativeness of the dispersions in those directions in the case of perfect conductors is just a result of our idealization and does not occur for real material boundaries.