Chasing Lambda

Recent astronomical observations of SNIa, CMB, as well as BAO in the Sloan Digital Sky Survey, suggest that the current Universe has entered a stage of an accelerated expansion with the transition redshift at $z \simeq 0.5$. While the simplest candidates to explain this fact is cosmological constant/vacuum energy, there exists a serious problem of coincidence. In theoretical cosmology we can find many possible approaches alleviating this problem by applying new physics or other conception of dark energy. We consider state of art candidates for the description of accelerating Universe in the framework of the Bayesian model selection. We point out advantages as well as troubles of this approach. We find that the combination of four data bases gives a stringent posterior probability of the $\Lambda$CDM model which is 74%. This fact is a quantitative exemplification of a turmoil in modern cosmology over the $\Lambda$ problem.Comment: Talk presented at the "A Century of Cosmology - Past, Present and Future" conference, S.Servolo(Venice), Italy, August 27-31 2007. To be published in Il Nuovo Ciment

Towards classification of simple dark energy cosmological models

We characterize a class of simple FRW models filled by both dark energy and dark matter in notion of a single potential function of the scale factor $a(t)$; $t$ is the cosmological time. It is representing potential of fictitious particle - Universe moving in 1-dimensional well $V(a)$ which the positional variable mimics the evolution of the Universe. Then the class of all dark energy models (called a multiverse) can be regarded as a Banach space naturally equipment in the structure of the Sobolev metric. In this paper we explore notion of $C^{1}$ metric introduced in the multiverse which measure distance between any two dark energy models. If we choose cold dark matter as a reference one then we can find how so far apart are different models offering explanation of present accelerating expansion phase of the Universe. We consider both models with dark energy (models with the generalized Chaplygin gas, models with variable coefficient equation of state $w_{X}=\frac{p_{X}}{\rho_{X}}$ parameterized by redshift $z$, models with phantom matter) as well as models basing on some modification of the Friedmann equation (Cardassian models, Dvali-Gabadadze-Porati brane models). We argue that because observational data still favor the $\Lambda$CDM model all reasonable dark energy models should belong to the nearby neighborhood of this model.Comment: 10 pages, 2 figures, the paper presented at 42nd Karpacz Winter School of Theoretical Physics: Ladek, Poland, 6-11 Feb 200

Testing and selection cosmological models with dark energy

It is described dynamics of a large class of accelerating cosmological models in terms of dynamical systems of the Newtonian type. The evolution of the models is reduced to the motion of a particle in a potential well parameterized by the scale factor. This potential function can be reconstructed from distant supernovae type Ia data and many cosmological models represented in terms of the potential becomes in a good agreement with current observational data. It is proposed to use the information criteria to overcome this degeneracy within a class of A) dark energy models and B) simple models basing on modification of the FRW equation. Two class of models can be recommended by the Akaike (AIC) and Schwarz (BIC) information criteria: the phantom and $\Lambda$CDM models.Comment: Talk at Albert Einstein Century International Conference at Palais de l'Unesco, Paris, France, 18-23 July 2005; to appear in the Proceedings; AIP style files included, 6 pages, 2 figure

Bayesian analysis of the backreaction models

We present the Bayesian analysis of four different types of backreation models, which are based on the Buchert equations. In this approach, one considers a solution to the Einstein equations for a general matter distribution and then an average of various observable quantities is taken. Such an approach became of considerable interest when it was shown that it could lead to agreement with observations without resorting to dark energy. In this paper we compare the LambdaCDM model and the backreation models with SNIa, BAO, and CMB data, and find that the former is favoured. However, the tested models were based on some particular assumptions about the relation between the average spatial curvature and the backreaction, as well as the relation between the curvature and curvature index. In this paper we modified the latter assumption, leaving the former unchanged. We find that, by varying the relation between the curvature and curvature index, we can obtain a better fit. Therefore, some further work is still needed -- in particular the relation between the backreaction and the curvature should be revisited in order to fully determine the feasibility of the backreaction models to mimic dark energy.Comment: Extended analysis compared to v1. Matches published version

Addition of Di(trimethylsilyl) Phosphite to Schiff Bases of 2,5-Diformylfuran

A series of 2,5-Furanyl-bis-(aminomethylphosphonic Acids) has been synthesized by the addition of di(trimethylsilyl) phosphite to azomethine bond of achiral Schiff bases derved from 2,5-diformylfuran. The stereochemical aspect of this reaction has been studied and compared with the behaviour of achiral terephthalic Schiff bases in similar reaction. Whereas, addition to achiral terephthalic Schiff bases was found to be highly stereoselective, the analogous reaction with achiral 2,5-diformylfuran Schiff bases was stereoselective exclusively in the case when the substituent is benzyl.N/

Alternating hemiplegia of childhood: New diagnostic options

A syndrome of alternating hemiplegia of childhood (AHC) is a rare disorder first presented in 1971. AHC is characterized by transient episodes of hemiplegia affecting either one or both sides of the body. Age of onset is before 18 months and the common earliest manifestations are dystonic or tonic attacks and nystagmus. Hemiplegic episodes last minutes to days and the frequency and duration tend to decrease with time. Motor and intellectual development is affected, deficits may also develop later. Epileptic seizures occur in some patients. Neuroimaging of the brain usually reveals no abnormalities. The variability of individual clinical presentations and evolution of symptoms have made diagnosis difficult. Therefore the problems of misdiagnosis could account for the low prevalence of this syndrome. This paper hopes to present actual data on AHC, especially of the results of genetic research and new diagnostic tools