Equation of state for Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This methods is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise the equation of state in the form $p=-\Lambda+w_{1}\rho(a)+w_{2}a^{\beta}+0$ and energy density $\rho=\Lambda+\rho_{01}a^{-3(1+w)}+\rho_{02}a^{\beta}+\rho_{03}a^{-3}$, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data. We showed that the model with scaling fluid fits well to supernovae data. We found that $\Omega_{\text{m},0} \simeq 0.4$ and $n \simeq -1$ ($\beta = -3n$), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that $\Omega_{\text{m},0}=0.3$ then the favoured model is close to concordance $\Lambda$CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in $\Lambda$CDM model, while intermediate distant SNIa should be fainter than in $\Lambda$CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over $\Lambda$CDM model. As a result we find from the Akaike model selection criterion prefers the model with noninteracting scaling fluid.Comment: accepted for publication versio

Anisotropy and inflation in Bianchi I brane worlds

After a more general assumption on the influence of the bulk on the brane, we extend some conclusions by Maartens et al. and Santos et al. on the asymptotic behavior of Bianchi I brane worlds. As a consequence of the nonlocal anisotropic stresses induced by the bulk, in most of our models, the brane does not isotropize and the nonlocal energy does not vanish in the limit in which the mean radius goes to infinity. We have also found the intriguing possibility that the inflation due to the cosmological constant might be prevented by the interaction with the bulk. We show that the problem for the mean radius can be completely solved in our models, which include as particular cases those in the references above.Comment: 10 pages, improved discussion on the likeliness of non-isotropization, completed list of references, matches version to appear in Class. Quantum Gra

Constraints on alternative models to dark energy

The recent observations of type Ia supernovae strongly support that the universe is accelerating now and decelerated in the recent past. This may be the evidence of the breakdown of the standard Friemann equation. We consider a general modified Friedmann equation. Three different models are analyzed in detail. The current supernovae data and the Wilkinson microwave anisotropy probe data are used to constrain these models. A detailed analysis of the transition from the deceleration phase to the acceleration phase is also performed.Comment: 10 pages, 1 figure, revtex

Fomin's conception of quantum cosmogenesis

The main aim of this paper is to extend the early approach to quantum cosmogenesis provided by Fomin. His approach was developed independently to the well-known Tryon description of the creation of the closed universe as a process of quantum fluctuation of vacuum. We apply the Fomin concept to derive the cosmological observables. We argue that Fomin's idea from his 1973 work, in contrast to Tryon's one has impact on the current Universe models and the proposed extension of his theory now can be tested by distant supernovae SNIa. Fomin's idea of the creation of the Universe is based on the intersection of two fundamental theories: general relativity and quantum field theory with the contemporary cosmological models with dark energy. As a result of comparison with contemporary approaches concerning dark energy, we found out that Fomin's idea appears in the context of the present acceleration of the Universe explanation: cosmological models with decaying vacuum. Contemporary it appears in the form of Ricci scalar dark energy connected with the holographic principle. We show also that the Fomin model admits the bounce instead of the initial singularity. We demonstrate that the Fomin model of cosmogenesis can be falsified and using SNIa data the values of model parameters is in agreement with observations.Comment: 12 pages, 4 figures; (v2) 22 pages, references added, figures improved; (v3) rewritten using revtex4; (v4) minor changes; (v5) improved formulas and extended statistical analysi

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

Constraints on accelerating universe using ESSENCE and Gold supernovae data combined with other cosmological probes

We use recently observed data: the 192 ESSENCE type Ia supernovae (SNe Ia), the 182 Gold SNe Ia, the 3-year WMAP, the SDSS baryon acoustic peak, the X-ray gas mass fraction in clusters and the observational $H(z)$ data to constrain models of the accelerating universe. Combining the 192 ESSENCE data with the observational $H(z)$ data to constrain a parameterized deceleration parameter, we obtain the best fit values of transition redshift and current deceleration parameter $z_{T}=0.632^{+0.256}_{-0.127}$, $q_{0}=-0.788^{+0.182}_{-0.182}$. Furthermore, using $\Lambda$CDM model and two model-independent equation of state of dark energy, we find that the combined constraint from the 192 ESSENCE data and other four cosmological observations gives smaller values of $\Omega_{0m}$ and $q_{0}$, but a larger value of $z_{T}$ than the combined constraint from the 182 Gold data with other four observations. Finally, according to the Akaike information criterion it is shown that the recently observed data equally supports three dark energy models: $\Lambda$CDM, $w_{de}(z)=w_{0}$ and $w_{de}(z)=w_{0}+w_{1}\ln(1+z)$.Comment: 18 pages, 8 figure

Dark energy problem: from phantom theory to modified Gauss-Bonnet gravity

The solution of dark energy problem in the models without scalars is presented. It is shown that late-time accelerating cosmology may be generated by the ideal fluid with some implicit equation of state. The universe evolution within modified Gauss-Bonnet gravity is considered. It is demonstrated that such gravitational approach may predict the (quintessential, cosmological constant or transient phantom) acceleration of the late-time universe with natural transiton from deceleration to acceleration (or from non-phantom to phantom era in the last case).Comment: LaTeX 8 pages, prepared for the Proceedings of QFEXT'05, minor correctons, references adde