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

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

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

Lyapunov function for cosmological dynamical system

We prove the asymptotic global stability of the de Sitter solution in the Friedmann-Robertson-Walker conservative and dissipative cosmology. In the proof we construct a Lyapunov function in an exact form and establish its relationship with the first integral of dynamical system determining evolution of the flat Universe. Our result is that de-Sitter solution is asymptotically stable solution for general form of equation of state p = (ρ, H), where dependence on the Hubble function H means that the effect of dissipation are included

BANKI PUBLICZNE JAKO INSTYTUCJE MOBILIZUJĄCE FINANSOWANIE GOSPODARKI NISKOEMISYJNEJ

Banki z dominującym udziałem kapitału państwowego, stwarzają możliwości realizacji założeń w zakresie zmian związanych z rozwojem zrównoważonym i ochroną klimatu. W Europie istnieje silna grupa tego typu instytucji bankowych, które realizują różnego rodzaju przedsięwzięcia o znaczeniu społecznym i środowiskowym. Instytucje te stają się coraz bardziej efektywnew przezwyciężaniu głównych barier inwestycyjnych oraz zakłóceń rynku, powstrzymujących inwestycje w niskoemisyjną gospodarkę.Banki państwowe są coraz lepiej przystosowane do transferów kapitału do niskoemisyjnej gospodarki. Mogą elastycznie dostosowywać się do pojawiających się wyzwań i dzięki temuwypracowywać wiele korzyści. Ich cztery kluczowe przewagi są następujące: umiejętność projektowania i implementacji finansowych mechanizmów dostosowanych do określonych celów, wykorzystanie bogatego doświadczenia i wiedzy z zakresu finansów i aspektów technicznych realizowanych przedsięwzięć, występowanie w roli pośredników i mediatorów w procesie realizacji niskoemisyjnych inwestycji oraz silna reputacja długoterminowych inwestorów w przedsięwzięcia o charakterze społecznym i środowiskowym.Celem artykułu jest przedstawienie działań podejmowanych przez wybrane instytucje bankowe, w kierunku rozwoju mechanizmu finansowania gospodarki niskoemisyjnej. Uzyskanewnioski zostały sformułowane na podstawie analizy działań siedmiu wybranych europejskich instytucji bankowych

Finite-temperature effective potential for an open universe

We investigate one-loop effects at finite temperatures for an open Robertson–Walker Universe, and v e obtain formulae for a scalar field Coleman-Weinterg potential. The meaning of non-zero temperature and negative curvature for the space-time topology R$^{1} \times$ PS$^{3}$ is discussed. Zero-point fluctuation of energy are determined

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

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

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