Wlodzimierz Godlowski

How many parameters in the cosmological models with dark energy

In cosmology many dramatically different scenarios with the past (big bang versus bounce) and in the future (de Sitter versus big rip) singularities are compatible with the present day observations. This difficulty is called the degeneracy problem. We use the Akaike and Bayesian information criteria of model selection to overcome this degeneracy and to determine a model with such a set of parameters which gives the most preferred fit to the SNIa data. We consider seven representative scenarios, namely: the CDM models with the cosmological constant, with topological defect, with phantom field, with bounce, with bouncing phantom field, with brane and model with the linear dynamical equation of state parameter. Applying the model selection information criteria we show that AIC indicates the flat phantom model while BIC indicates both flat phantom and flat

Constraints on cosmological models from strong gravitational lensing systems

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Generalized Chaplygin Gas Models Tested with Type Ia Supernovae

CDM models. Finally we conclude that the number of essential parameters chosen by dark energy models which are compared with SNIa data is two.Abstract In cosmology many dramatically different scenarios in the past (big bang versus bounce) and in the future (de Sitter versus big rip) are compatible with the present day observations. This difficulties are called the degeneracy problem. We use the Akaike (AIC) and Bayesian (BIC) information criteria of model selection to avoid this degeneracy and to determine the model with such a set of parameters which gives the most preferred fit to the data. We consider seven representative scenarios, namely: the ΛCDM, CDM model with topological defect, phantom CDM model, bouncing ΛCDM model, bouncing phantom CDM model, brane ΛCDM model and model with the dynamical equation of state parameter linearized around the present epoch. Applying the information criteria to the currently available SNIa data we show that AIC indicates the flat phantom model while BIC indicates both flat phantom CDM and flat ΛCDM models. Finally we conclude that number of essential parameters chosen by dark energy models which are compared with SNIa data is two.

Which cosmological model—with dark energy or modified FRW dynamics?

Strong lensing has developed into an important astrophysical tool for probing both cosmology and galaxies (their structure, formation, and evolution). Using the gravitational lensing theory and cluster mass distribution model, we try to collect a relatively complete observational data concerning the Hubble constant independent ratio between two angular diameter distances Dds/Ds from various large systematic gravitational lens surveys and lensing by galaxy clusters combined with X-ray observations, and check the possibility to use it in the future as complementary to other cosmological probes. On one hand, strongly gravitationally lensed quasar-galaxy systems create such a new opportunity by combining stellar kinematics (central velocity dispersion measurements) with lensing geometry (Einstein radius determination from position of images). We apply such a method to a combined gravitational lens data set including 70 data points from Sloan Lens ACS (SLACS) and Lens Structure and Dynamics survey (LSD). On the other hand, a new sample of 10 lensing galaxy clusters with redshifts ranging from 0.1 to 0.6 carefully selected from strong gravitational lensing systems with both X-ray satellite observations and optical giant luminous arcs, is also used to constrain three dark energy models (ΛCDM, constant w and CPL) under a flat universe assumption. For the full sample (n = 80) and the restricted sample (n = 46) including 36 two-image lenses and 10 strong lensing arcs, we obtain relatively good fitting values of basic cosmological parameters, which generally agree with the results already known in the literature. This results encourages further development of this method and its use on larger samples obtained in the future.

Accelerated cosmological models in modified gravity tested by distant supernovae SNIa data

The generalized Chaplygin gas (GCG), with the equation of state p = -A/ρα, was recently proposed as a candidate for dark energy in the universe. In this paper we confront the GCG with Type Ia supernova (SN Ia) data using available samples. Specifically, we have tested the GCG cosmology in three different classes of models with (1) Ωm = 0.3 and ΩCh = 0.7, (2) Ωm = 0.05 and ΩCh = 0.95, and (3) Ωm = 0 and ΩCh = 1, as well as a model without prior assumptions on Ωm. The best-fit models are obtained by minimizing the χ2 function. We supplement our analysis with confidence intervals in the (A0, α)-plane by marginalizing the probability density functions (pdfs) over the remaining parameters assuming uniform priors. We have also derived one-dimensional pdfs for ΩCh obtained from joint marginalization over α and A0. The maximum value of such a pdf provides the most probable value of ΩCh within the full class of GCG models. The general conclusion is that SN Ia data give support to the Chaplygin gas (with α = 1). However, a noticeable preference for A0-values close to 1 means that the α dependence becomes insignificant. This is reflected in one-dimensional pdfs for α that turned out to be flat, meaning that the power of the present supernova data to discriminate between various GCG models (differing by α) is weak. Extending our analysis by relaxing the prior assumption of the flatness of the universe leads to the result that even though the best-fit values of Ωk are formally nonzero, they are still close to the flat case. Our results show clearly that in GCG cosmology, distant (i.e., z > 1) supernovae should be brighter than in the ΛCDM model. Therefore, one can expect that future supernova experiments (e.g., SNAP) having access to higher redshifts will eventually resolve the issue of whether the dark energy content of the universe could be described as a Chaplygin gas. Moreover, it would be possible to differentiate between models with various values of the α-parameter and/or discriminate between GCG, Cardassian, and ΛCDM models. This discriminative power of the forthcoming mission has been demonstrated on simulated SNAP data.

Constraints on a Cardassian Model from Type Ia Supernova Data, Revisited

Abstract Recent measurements of distant type Ia supernovae (SNIa), as well as other observations, indicate that our universe is in an accelerating phase of expansion. In principle, there are two alternative explanations for such an acceleration (there is also a possibility that the acceleration can be driven by inhomogenities in cosmological models). The first approach postulates an unknown form of energy violating the strong energy condition, while the second postulates some modification of FRW dynamics. Both approaches agree well with present-day observations which results in the difficulty of choosing the model. We use the Akaike (AIC) and Bayesian (BIC) information criteria of model selection to overcome this degeneracy and to determine a model with a set of parameters which gives the most preferred fit to the SNIa data. We consider five representative evolutionary scenarios in each of the groups. Among the dark energy proposals are the Λ CDM model, the CDM model with phantom field, CDM model with topological defect, a model with the Chaplygin gas, and a model with a linear dynamical equation of state parameter. As alternative prototype scenarios we consider: the brane world Dvali–Gabadadze–Porrati scenario, brane models in Randall–Sundrum scenario, Cardassian models with dust matter and radiation, a bouncing model with the cosmological constant and metric-affine gravity (MAG) inspired cosmological models. Applying the model selection criteria, we show that both AIC and BIC indicate that additional contributions arising from non-standard FRW dynamics are not necessary to explain SNIa. Adopting the model selection information criteria, we show that the AIC indicates the flat phantom model while BIC indicates both flat phantom and flat Λ CDM models.

Letter: Rotation of the Universe and the Angular Momenta of Celestial Bodies

Recent type Ia supernova measurements and other astronomical observations suggest that our Universe is, at the present epoch, in an accelerating phase of evolution. While a dark energy of unknown form and origin is usually proposed as the most feasible mechanism for the acceleration, there appeared some generalizations of Einstein equations which could mimic dark energy. In this work we investigate observational constraints on a modified Friedmann equation obtained from the generalized Lagrangian L{proportional_to}R{sup n} minimally coupled with matter via the Palatini first-order formalism. We mainly concentrate on such restrictions of model parameters which can be derived from distant supernovae and baryon oscillation tests. We obtain confidence levels for two parameters (n, {omega}{sub m,0}) and find, from combined analysis, that the preferred value of {omega}{sub m,0} equals 0.3. For deeper statistical analysis and for comparison of our model with predictions of the {lambda}CDM concordance model, one applies Akaike and Bayesian information criteria of model selection. Finally, we conclude that the Friedmann-Robertson-Walker model merged with a first-order nonlinear gravity survives SNIa and baryon oscillation tests.

REMARKS ON THE METHODS OF INVESTIGATIONS OF ALIGNMENT OF GALAXIES

We discuss some observational constraints, resulting from Type Ia supernova (SN Ia) observations, imposed on the behavior of the original flat Cardassian model and on its extension with the curvature term included. We test the models using the Perlmutter SN Ia data, as well as the new Knop and Tonry samples. We estimate the Cardassian model parameters using the best-fit procedure and the likelihood method. In the fitting procedure we use density variables for matter, Cardassian fluid, and curvature and include the errors in redshift measurement. For the Perlmutter sample in the nonflat Cardassian model we obtain a high-density or normal (Ωm,0 ≈ 0.3) universe, while for the flat Cardassian model we have a high-density universe. For sample A in the high-density universe, we find negative values of estimates of n, which can be interpreted as a phantom fluid effect. For the likelihood method we find that a nearly flat universe is preferred. We show that if we assume that matter density is 0.3, then n ≈ 0 in the flat Cardassian model, which corresponds to the Perlmutter model with a cosmological constant. Tests with the Knop and Tonry SN Ia samples show no significant differences in results.

BRANE UNIVERSES TESTED AGAINST ASTRONOMICAL DATA

We discuss the equation of motion of the rotating homogenous and isotropic model of the Universe. We show that the model predicts the presence of a minimum in the relation between the mass of an astronomical object and its angular momentum. We show that this relation appears to be universal, and we predict the masses of structures with minimal angular momenta in agreement with observations. In such a manner we suggest the possibility at acquirement of angular momenta of celestial bodies during their formation from the global rotation of the Universe.

Some remarks on the angular momenta of galaxies, their clusters and superclusters

In the 1975 Hawley and Peebles proposed the use of three statistical tests for investigations of galaxy orientations in the large structures. Nowadays, it is considered as the standard method of searching for galactic alignments. In the present paper we analyzed the tests in detail and proposed a few improvements. Based on the improvements, a new method of analysis of the alignment of galaxies in clusters is proposed. The power of this method is demonstrated on the sample of 247 Abell clusters with at least 100 objects in each. The distributions of the position angles for galaxies in each cluster are analyzed using statistical tests: χ2, Fourier, autocorrelation, and Kolmogorov test. The mean value of analyzed statistics is compared with theoretical predictions as well as with results obtained from numerical simulations. We performed 1000 simulations of 247 fictitious clusters, each with the numbers of galaxies the same as in the real clusters. We found that orientations of galaxies in analyzed clusters are not random, i.e., that there exists an alignment of galaxies in rich Abell galaxy clusters.