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

On the viability of local criteria for chaos

We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor sufficient for the occurrence of chaos. To this purpose, we introduce a class of chaotic two-dimensional systems with Gaussian curvature everywhere positive and, hence, locally stable. We show explicitly that chaotic behavior arises from some trajectories that reach certain non convex parts of the boundary of the effective Riemannian manifold. Our result questions, once more, the viability of local, curvature-based criteria to predict chaotic behavior.Comment: 10 page

Emerging singularities in the bouncing loop cosmology

In this paper we calculate $\mathcal{O}(\mu^4)$ corrections from holonomies in the Loop Quantum Gravity, usually not taken into account. Allowance of the corrections of this kind is equivalent with the choice of the new quatization scheme. Quantization ambiguities in the Loop Quantum Cosmology allow for this additional freedom and presented corrections are consistent with the standard approach. We apply these corrections to the flat FRW cosmological model and calculate the modified Friedmann equation. We show that the bounce appears in the models with the standard $\mathcal{O}(\mu^2)$ quantization scheme is shifted to the higher energies $\rho_{\text{bounce}} = 3 \rho_{\text{c}}$. Also a pole in the Hubble parameter appears for $\rho_{\text{pole}} = {3/2} \rho_{\text{c}}$ corresponding to \emph{hyper-inflation/deflation} phases. This pole represents a curvature singularity at which the scale factor is finite. In this scenario the singularity and bounce co-exist. Moreover we find that an ordinary bouncing solution appears only when quantum corrections in the lowest order are considered. Higher order corrections can lead to the nonperturbative effects.Comment: RevTeX4, 8 pages, 4 figures; v2 change of title, more discussion on co-existence of singularity and bounc

Model jako punkt wyjścia dla małej formy w wideo-art

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The problem of effectiveness of classical dimensional reduction mechanism in homogeneous arbitrary-dimensional cosmology

Thermodynamical functions are determined for the bosonic gas distribution in the external gravitational field described by multidimensional cosmological models having the structure FRW $\times$ B$^{D}$, where B$^{D}$ is any D-dimensional compact space with the scalar curvature R$^{(D)}$. Universal asymptotics of this function are found for the following situations: 1) at high temperatures, with $\beta^{2}$R $\ll$ 1 and $\beta m_{0} \ll$ 1, 2) at low temperatures, with $\beta^{2}$R $\gg$ 1 and $\beta m_{0} \gg$ 1, where R is the scale factor of the physical space, and is the reciprocal of temperature. It is shown that if R$^{(3)}$ / R$^{(D)} \gg$ 1 (where R$^{(3)}$ and R$^{(D)}$ are curvature scalars of macro- and microspace, correspondingly), the Casimir energy is always negative. These results are applied to discuss the dimensional reduction generated by the classical Einstein equations with quantum corrections. The idea of the dynamical dimensional reduction is expressed, in terms of the dynamical system theory, as the problem of the existence of a single stable critical point representing a configuration with the static internal space. It is demonstrated that, in the low-temperature approximation, there is no effective mechanism of the dimensional reduction to a static internal space, if B$^{D}$ is a group manifold (with the same scale factor in all internal directions). On the other hand, the effective mechanism of the dimensional reduction to the zero size does exist. The existence of such mechanism for the full class of multidimensional homogeneous cosmologies with the hydrodynamic energy-momentum tensor is also discussed

Computer in teaching physical experiment at a high school and university level

The advantages of the use of the on line physics experiments are presented on the example of Adam Mickiewicz University. The use of MBL technique in new areas is proposed. New solution for school and distant learning are presented

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

Dark matter and dark energy as a effects of Modified Gravity

We explain the effect of dark matter (flat rotation curve) using modified gravitational dynamics. We investigate in this context a low energy limit of generalized general relativity with a nonlinear Lagrangian ${\cal L}\propto R^n$, where $R$ is the (generalized) Ricci scalar and $n$ is parameter estimated from SNIa data. We estimate parameter $\beta$ in modified gravitational potential $V(r) \propto -\frac{1}{r}(1+(\frac{r}{r_c})^{\beta})$. Then we compare value of $\beta$ obtained from SNIa data with $\beta$ parameter evaluated from the best fitted rotation curve. We find $\beta \simeq 0.7$ which becomes in good agreement with an observation of spiral galaxies rotation curve. We also find preferred value of $\Omega_{m,0}$ from the combined analysis of supernovae data and baryon oscillation peak. We argue that although amount of "dark energy" (of non-substantial origin) is consistent with SNIa data and flat curves of spiral galaxies are reproduces in the framework of modified Einstein's equation we still need substantial dark matter. For comparison predictions of the model with predictions of the $\Lambda$CDM concordance model we apply the Akaike and Bayesian information criteria of model selection.Comment: Lectures given at 42nd Karpacz Winter School of Theoretical Physics: Ladek, Poland, 6-11 Feb 200

Towards testing interacting cosmology by distant type Ia supernovae

We investigate the possibility of testing cosmological models with interaction between matter and energy sector. We assume the standard FRW model while the so called energy conservation condition is interpreted locally in terms of energy transfer. We analyze two forms of dark energy sectors: the cosmological constant and phantom field. We find a simple exact solution of the models in which energy transfer is described by a Cardassian like term in the relation of $H^{2}(z)$, where $H$ is Hubble's function and $z$ is redshift. The considered models have two additional parameters $(\Omega_{\text{int}},n)$ (apart the parameters of the $\Lambda$CDM model) which can be tested using SNIa data. In the estimation of the model parameters Riess et al.'s sample is used. We also confront the quality of statistical fits for both the $\Lambda$CDM model and the interacting models with the help of the Akaike and Bayesian informative criteria. Our conclusion from standard best fit method is that the interacting models explains the acceleration of the Universe better but they give rise to a universe with high matter density. However, using the tools of information criteria we find that the two new parameters play an insufficient role in improving the fit to SNIa data and the standard $\Lambda$CDM model is still preferred. We conclude that high precision detection of high redshift supernovae could supply data capable of justifying adoption of new parameters.Comment: RevTeX4, 14 pages, 7 figure

Asymmetric cyclic evolution in polymerised cosmology

The dynamical systems methods are used to study evolution of the polymerised scalar field cosmologies with the cosmological constant. We have found all evolutional paths admissible for all initial conditions on the two-dimensional phase space. We have shown that the cyclic solutions are generic. The exact solution for polymerised cosmology is also obtained. Two basic cases are investigated, the polymerised scalar field and the polymerised gravitational and scalar field part. In the former the division on the cyclic and non-cyclic behaviour is established following the sign of the cosmological constant. The value of the cosmological constant is upper bounded purely from the dynamical setting.Comment: 10 pages, 4 figs, JHEP3.cl