Generalized Chaplygin Gas Models tested with SNIa

The so called Generalized Chaplygin Gas (GCG) with the equation of state $p = - \frac{A}{{\rho}^{\alpha}}$ was recently proposed as a candidate for dark energy in the Universe. In this paper we confront the GCG with SNIa data. Specifically we have tested the GCG cosmology in three different classes of models with (1) $\Omega_m= 0.3$, $\Omega_{Ch}= 0.7$; (2) $\Omega_m= 0.05$, $\Omega_{Ch}= 0.95$ and (3) $\Omega_m = 0$, $\Omega_{Ch} = 1$, as well as the model withouth any assumption on $\Omega_m$. The best fitted models are obtained by minimalizing the $\chi^2$ function and $\chi^2$ levels in the $(A_0, \alpha)$ plane. We supplemented our analysis with confidence intervals in the $(A_0, \alpha)$ plane, as well as one-dimensional probability distribution functions for models parameter. The general conclusion is that SNIa data strongly support the Chaplygin gas (with $\alpha = 1$). Extending our analysisby relaxing the flat prior lead to the result that even though the best fitted values of $\Omega_k$ are formally non-zero, still they are close to flat case. It should be viewed as an advantage of the GCG model since in similar analysisof $\Lambda$CDM model high negative value of $\Omega_{k}$ were found to be bestfitted to the data and independent inspiration from CMBR and extragalactic astronomy has been invoked to fix the curvature problem. Our results show clearly that in Generalized Chaplygin Gas cosmology distant $z >1$ supernovae should be brighter than in $\Lambda$CDM model.This prediction seems to be confirmed with new Riess high redshift SNIa sample. Moreover, we argue that with the future SNAP data it would be possible to differentiate between models with various value of $\alpha$ parameter and/or discriminated between GCG, Cardassian and $\Lambda$CDM modelsComment: 54 pages 29 figures improved version analysis flat prior relaxed high redshift Riess SNIa sample include

Dynamical dimensional reduction in multidimensional Bianchi I models

We discuss some mechanisms of isotropization in the class of n-dimensional Bianchi I models. We show that these models can isotropize but this process leads to the breakdown of dimensional reduction. Thus we ought to look for such a mechanism of dimensional reduction that isotropizes the space

Dynamical meaning of the adiabatic quantum phase

The interaction between the "macrosystem" (corresponding to the so-called slow variables) and the "microsystem" (corresponding to the so-called fast variables) is considered. By using the Born–Oppenheimer adiabatic approximation it is shown that such interaction modifies dynamics of the "macrosystem". We find the form of modified Poisson brackets for the "macrosystem". We also show how symmetries and laws of conservation of the "macrosystem" are influenced by this interaction

Lorentz Invariance Violation induced time delays in GRBs in different cosmological models

Lorentz Invariance Violation (LIV) manifesting itself by energy dependent modification of standard relativistic dispersion relation has recently attracted a considerable attention. Ellis et al. previously investigated the energy dependent time offsets in different energy bands on a sample of gamma ray bursts and, assuming standard cosmological model, they found a weak indication for redshift dependence of time delays suggestive of LIV. Going beyond the $\Lambda$CDM cosmology we extend this analysis considering also four alternative models of dark energy (quintessence with constant and variable equation of state, Chaplygin gas and brane-world cosmology). It turns out that the effect noticed by Ellis et al. is also present in those models and is the strongest for quintessence with variable equation of state.Comment: 14 pages, 1 figur

Cosmic Equation of State and Advanced LIGO Type Gravity Wave Experiments

Future generation of interferometric gravitational wave detectors is hoped to provide accurate measurements of the final stages of binary inspirals. The sources probed by such experiments are of extragalactic origin and the observed chirp mass is the intrinsic chirp mass multiplied by $(1+z)$ where $z$ is the redshift of the source. Moreover the luminosity distance is a direct observable is such experiments. This creates the possibility to establish a new kind of cosmological tests, supplementary to more standard ones. Recent observations of distant type Ia supernovae light-curves suggest that the expansion of the universe has recently begun to accelerate. A popular explanation of present accelerating expansion of the universe is to assume that some part $\Omega_Q$ of the matter-energy density is in the form of dark component called ``the quintessence'' with the equation of state $p_Q = w \rho_Q$ with $w \geq -1.$ In this paper we consider the predictions concerning observations of binary inspirals in future LIGO type interferometric experiments assuming a ``quintessence cosmology''. In particular we compute the expected redshift distributions of observed events in the a priori admissible range of parameters describing the equation of state for the quintessence. We find that this distribution has a robust dependence on the cosmic equation of state.Comment: 10 pages, Latex plus 5 figures.MNRAS accepte

Dynamical System Approach to Cosmological Models with a Varying Speed of Light

Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state. The solutions are analyzed on two-dimensional phase space in the variables $(x, \dot{x})$ where $x$ is a function of a scale factor $a$. Then we show how the horizon problem may be solved on some evolutional paths. It is shown that the models with negative curvature overcome the horizon and flatness problems. The presented method of reduction can be adopted to the analysis of dynamics of the universe with the general form of the equation of state $p=\gamma(a)\epsilon$. This is demonstrated using as an example the dynamics of VSL models filled with a non-interacting fluid. We demonstrate a new type of evolution near the initial singularity caused by a varying speed of light. The singularity-free oscillating universes are also admitted for positive cosmological constant. We consider a quantum VSL FRW closed model with radiation and show that the highest tunnelling rate occurs for a constant velocity of light if $c(a) \propto a^n$ and $-1 < n \le 0$. It is also proved that the considered class of models is structurally unstable for the case of $n < 0$.Comment: 18 pages, 5 figures, RevTeX4; final version to appear in PR

The reliability of the AIC method in Cosmological Model Selection

The Akaike information criterion (AIC) has been used as a statistical criterion to compare the appropriateness of different dark energy candidate models underlying a particular data set. Under suitable conditions, the AIC is an indirect estimate of the Kullback-Leibler divergence D(T//A) of a candidate model A with respect to the truth T. Thus, a dark energy model with a smaller AIC is ranked as a better model, since it has a smaller Kullback-Leibler discrepancy with T. In this paper, we explore the impact of statistical errors in estimating the AIC during model comparison. Using a parametric bootstrap technique, we study the distribution of AIC differences between a set of candidate models due to different realizations of noise in the data and show that the shape and spread of this distribution can be quite varied. We also study the rate of success of the AIC procedure for different values of a threshold parameter popularly used in the literature. For plausible choices of true dark energy models, our studies suggest that investigating such distributions of AIC differences in addition to the threshold is useful in correctly interpreting comparisons of dark energy models using the AIC technique.Comment: Figures and further discussions of the results were added, and the version matches the version published in MNRA

CONSTRAINTS ON NON-FLAT COSMOLOGIES WITH MASSIVE NEUTRINOS AFTER PLANCK 2015

Citation: Chen, Y., Ratra, B., Biesiada, M., Li, S., & Zhu, Z. H. (2016). CONSTRAINTS ON NON-FLAT COSMOLOGIES WITH MASSIVE NEUTRINOS AFTER PLANCK 2015. Astrophysical Journal, 829(2), 7. doi:10.3847/0004-637x/829/2/61We investigate two dark energy cosmological models (i.e., the Lambda CDM and phi CDM models) with massive neutrinos assuming two different neutrino mass hierarchies in both the spatially flat and non-flat scenarios, where in the phi CDM model the scalar field possesses an inverse power-law potential, V(phi) proportional to phi(-alpha) (alpha > 0). Cosmic microwave background data from Planck. 2015, baryon acoustic oscillation data from 6dFGS, SDSS-MGS, BOSS-LOWZ and BOSS CMASS-DR11, the joint light-curve analysis compilation of SNe Ia apparent magnitude observations, and the Hubble Space Telescope H-0 prior, are jointly employed to constrain the model parameters. We first determine constraints assuming three species of degenerate massive neutrinos. In the spatially flat (non-flat) Lambda CDM model, the sum of neutrino masses is bounded as Sigma m(nu) < 0.165(0.299) eV at 95% confidence level (CL). Correspondingly, in the flat (non-flat) phi CDM model, we find Sigma m(nu) < 0.164(0.301) eV at 95% CL. The inclusion of spatial curvature as a free parameter results in a significant broadening of confidence regions for Sigma m(nu) igenstate, we obtain similar conclusions to those obtained in the degenerate neutrino mass scenario. In addition, the results show that the bounds on Sigma m(nu) based on two different neutrino mass hierarchies have insignificant differences in the spatially flat case for both the Lambda CDM and phi CDM models; however, the corresponding differences are larger in the nonflat case