Dark energy FRW cosmology - dynamical system reconstruction

We develop a simple method of dark energy reconstruction using a geometrical form of the luminosity-distance relation. In this method the FRW dynamical system with dark energy is reconstructed instead of the equation of state parameter. We give several examples which illustrate the usefulness of our method in fitting the redshift transition from the decelerating to accelerating phase as the value of the Hubble function at the transition.Comment: Talk presented at Spanish Relativity Meeting 2007, Puerto de la Cruz, Tenerife, Spain, 10-14 September 200

Observational hints on the Big Bounce

In this paper we study possible observational consequences of the bouncing cosmology. We consider a model where a phase of inflation is preceded by a cosmic bounce. While we consider in this paper only that the bounce is due to loop quantum gravity, most of the results presented here can be applied for different bouncing cosmologies. We concentrate on the scenario where the scalar field, as the result of contraction of the universe, is driven from the bottom of the potential well. The field is amplified, and finally the phase of the standard slow-roll inflation is realized. Such an evolution modifies the standard inflationary spectrum of perturbations by the additional oscillations and damping on the large scales. We extract the parameters of the model from the observations of the cosmic microwave background radiation. In particular, the value of inflaton mass is equal to $m=(2.6 \pm 0.6) \cdot 10^{13}$ GeV. In our considerations we base on the seven years of observations made by the WMAP satellite. We propose the new observational consistency check for the phase of slow-roll inflation. We investigate the conditions which have to be fulfilled to make the observations of the Big Bounce effects possible. We translate them to the requirements on the parameters of the model and then put the observational constraints on the model. Based on assumption usually made in loop quantum cosmology, the Barbero-Immirzi parameter was shown to be constrained by $\gamma<1100$ from the cosmological observations. We have compared the Big Bounce model with the standard Big Bang scenario and showed that the present observational data is not informative enough to distinguish these models.Comment: 25 pages, 8 figures, JHEP3.cl

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

Uniting cosmological epochs through the twister solution in cosmology with non-minimal coupling

We investigate dynamics of a flat FRW cosmological model with a barotropic matter and a non-minimally coupled scalar field (both canonical and phantom). In our approach we do not assume any specific form of a potential function for the scalar field and we are looking for generic scenarios of evolution. We show that dynamics of universe can be reduced to a 3-dimensional dynamical system. We have found the set of fixed points and established their character. These critical points represent all important epochs in evolution of the universe : (a) a finite scale factor singularity, (b) an inflation (rapid-roll and slow-roll), (c) a radiation domination, (d) a matter domination and (e) a quintessence era. We have shown that the inflation, the radiation and matter domination epochs are transient ones and last for a finite amount of time. The existence of the radiation domination epoch is purely the effect of a non-minimal coupling constant. We show the existence of a twister type solution wandering between all these critical points.Comment: 22 pages, 5 figs; (v2.) 27 pages, 12 figs, JCAP in pres

Scalar field cosmology in the energy phase-space -- unified description of dynamics

In this letter we apply dynamical system methods to study all evolutional paths admissible for all initial conditions of the FRW cosmological model with a non-minimally coupled to gravity scalar field and a barotropic fluid. We choose "energy variables" as phase variables. We reduce dynamics to a 3-dimensional dynamical system for an arbitrary potential of the scalar field in the phase space variables. After postulating the potential parameter $\Gamma$ as a function of $\lambda$ (defined as $-V'/V$) we reduce whole dynamics to a 3-dimensional dynamical system and study evolutional paths leading to current accelerating expansion. If we restrict the form of the potential then we will obtain a 2-dimensional dynamical system. We use the dynamical system approach to find a new generic quintessence scenario of approaching to the de Sitter attractor which appears only for the case of non-vanishing coupling constant.Comment: revtex4, 16 pages, 3 figs; (v2) refs. added, published versio

AIC, BIC, Bayesian evidence against the interacting dark energy model

Recent astronomical observations have indicated that the Universe is in the phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting $\Lambda$CDM model where the interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative---the $\Lambda$CDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam's principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: SNIa (Union2.1), $h(z)$, BAO, Alcock--Paczynski test and CMB we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting $\Lambda$CDM model when compared to the $\Lambda$CDM model, while those based on the BIC indicated that there is the strong evidence against it in favor the $\Lambda$CDM model. Given the weak or almost none support for the interacting $\Lambda$CDM model and bearing in mind Occam's razor we are inclined to reject this model.Comment: LaTeX svjour3, 12 pages, 3 figure