arXiv subjects

Marek Szydlowski

Publications and source records attributed to Marek Szydlowski.

At least 91 records · Page 5Linked to original sources

arXiv2006

On Capital Dependent Dynamics of Knowledge

We investigate the dynamics of growth models in terms of dynamical system theory. We analyse some forms of knowledge and its influence on economic growth. We assume that the rate of change of knowledge depends on both the rate of change of physical and human capital. First, we study model with constant savings. The model with optimised behaviour of households is also considered. We show that the model where the rate of change of knowledge depends only on the rate of change of physical capital can be reduced to the form of the two-dimensional autonomous dynamical system. All possible evolutional paths and the stability of solutions in the phase space are discussed in details. We obtain that the rate of growth of capital, consumption and output are greater in the case of capital dependent rate of change of knowledge.

physics.soc-ph↗

arXiv2006

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 $w_{X}=\frac{p_{X}}{ρ_{X}}$ 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 $Λ$CDM model all reasonable dark energy models should belong to the nearby neighborhood of this model.

gr-qc↗

arXiv2006

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 $β$ in modified gravitational potential $V(r) \propto -\frac{1}{r}(1+(\frac{r}{r_c})^β)$. Then we compare value of $β$ obtained from SNIa data with $β$ parameter evaluated from the best fitted rotation curve. We find $β\simeq 0.7$ which becomes in good agreement with an observation of spiral galaxies rotation curve. We also find preferred value of $Ω_{m,0}$ 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 $Λ$CDM concordance model we apply the Akaike and Bayesian information criteria of model selection.

astro-ph↗

arXiv2006

Accelerated Cosmological Models in Modified Gravity tested by distant Supernovae SNIa data

Recent supernovae of type Ia measurements and other astronomical observations suggest that our universe is in accelerating phase of evolution at the present epoch. While a dark energy of unknown form is usually proposed as the most feasible mechanism for the acceleration, there are appears some alternative conception that some effects arising from generalization of Einstein equation can mimic dark energy through a modified Friedmann equation. In this work we investigate some observational constraints on modified Friedmann equation obtained from generalized Lagrangian ${\cal L} \propto R^n$ in minimal coupling with matter in Palatini formalism. We mainly concentrate on the constraints of model parameters from distant supernovae but other constraint from baryon oscillation prior is also considered. We obtain the confidence levels on two additional model parameter ($n$,$Ω_{m,0}$). We conclude that the FRW model of First-Order Non-linear gravity survives several observational test like SNIa observation and baryon oscillation peaks. We find preferred value of $Ω_{m,0} \simeq 0.3$ from combined analysis of supernovae data and baryon oscillation peak. For deeper statistical analysis we apply Akaike and Bayesian information criteria of model selection for comparison prediction of the model with prediction of concordance $Λ$CDM model.

astro-ph↗

arXiv2006

Top ten accelerating cosmological models

Recent astronomical observations indicate that the Universe is presently almost flat and undergoing a period of accelerated expansion. Basing on Einstein's general relativity all these observations can be explained by the hypothesis of a dark energy component in addition to cold dark matter (CDM). Because the nature of this dark energy is unknown, it was proposed some alternative scenario to explain the current accelerating Universe. The key point of this scenario is to modify the standard FRW equation instead of mysterious dark energy component. The standard approach to constrain model parameters, based on the likelihood method, gives a best-fit model and confidence ranges for those parameters. We always arbitrary choose the set of parameters which define a model which we compare with observational data. Because in the generic case, the introducing of new parameters improves a fit to the data set, there appears the problem of elimination of model parameters which can play an insufficient role. The Bayesian information criteria of model selection (the AIC and BIC) are dedicated to promotion a set of parameters which should be incorporated to the model. We divide class of all accelerating cosmological models into two groups according to the two types of explanation acceleration of the Universe. Then the Bayesian framework of model selection is used to determine the set of parameters which gives preferred fit to the SNIa data. We find a few of flat cosmological models which can be recommend by both the Bayes factor and Akaike information criterion.

astro-ph↗

arXiv2006

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 $p=-Λ+w_{1}ρ(a)+w_{2}a^β+0$ and energy density $ρ=Λ+ρ_{01}a^{-3(1+w)}+ρ_{02}a^β+ρ_{03}a^{-3}$, 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 $Ω_{\text{m},0} \simeq 0.4$ and $n \simeq -1$ ($β= -3n$), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that $Ω_{\text{m},0}=0.3$ then the favoured model is close to concordance $Λ$CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in $Λ$CDM model, while intermediate distant SNIa should be fainter than in $Λ$CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over $Λ$CDM model. As a result we find from the Akaike model selection criterion prefers the model with noninteracting scaling fluid.

astro-ph↗

arXiv2006

Can brane dark energy model be probed observationally by distant supernovae?

The recent astronomical measurements of distant supernovae as well as other observations indicate that our universe is presently accelerating. There are different proposals for the explanation of this acceleration, such as the cosmological constant $Λ$, decaying vacuum energy, an evolving scalar field (quintessence), phantom energy, etc. Most of these proposals require the existence of exotic matter with negative pressure violating the strong energy condition. On the other hand, there have appeared many models which offer dramatically different mechanisms for the current acceleration, in which dark energy emerges from the gravity sector rather than from the matter sector. In this paper, we compare the concordance $Λ$CDM model with the Sahni-Shtanov brane-world models of dark energy by using the Akaike and Bayesian information criteria. We show that new parameters in the brane model are not statistically significant in terms of the information criteria, although the best fit method gives an improved fit to the SNIa data, because of the additional parameters. This is because the information criteria of model selection compensate for this advantage by penalizing models having more free parameters. We conclude that only new future observational data are accurate enough to give an advantage to dark-energy models of the brane origin, i.e., a very high-significance detection is required to justify the presence of new parameters. In our statistical analysis both Riess et al.'s and Astier et al.'s SNIa samples are used. For stringent constraining parameters of the models the baryon oscillation peak (BOP) test is used.

astro-ph↗

arXiv2006

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 $Λ$CDM models.

astro-ph↗

arXiv2006

Non-integrability of density perturbations in the FRW universe

We investigate the evolution equation of linear density perturbations in the Friedmann-Robertson-Walker universe with matter, radiation and the cosmological constant. The concept of solvability by quadratures is defined and used to prove that there are no "closed form" solutions except for the known Chernin, Heath, Meszaros and simple degenerate ones. The analysis is performed applying Kovacic's algorithm. The possibility of the existence of other, more general solutions involving special functions is also investigated.

gr-qc↗

arXiv2005

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 $(Ω_{\text{int}},n)$ (apart the parameters of the $Λ$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 $Λ$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 $Λ$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.

astro-ph↗

arXiv2005

Phantom cosmology as a simple model with dynamical complexity

We study the Friedmann-Robertson-Walker model with phantom fields modelled in terms of scalar fields. We apply the Ziglin theory of integrability and find that the flat model is nonintegrable. Then we cannot expect to determine simple analytical solutions of the Einstein equations. We demonstrate that there is only a discrete set of parameters where this model is integrable. For comparison we describe the phantoms fields in terms of the barotropic equation of state. It is shown that in the contrast to the phantoms modelled as scalar fields, the dynamics is always integrable and phase portraits are constructed. In this case we find the duality relation.

astro-ph↗

arXiv2005

Which cosmological models -- with dark energy or modified FRW dynamics?

Recent measurements of distant type Ia supernovae (SNIa) as well as other observations indicate that our universe is in accelerating phase of expansion. In principle there are two alternative explanation for such an acceleration. While in the first approach an unknown form of energy violating the strong energy condition is postulated, in second one some modification of FRW dynamics is postulated. The both approaches are in well agreement with present day observations which is the manifestation of the degeneracy problem appearing in observational cosmology. We use the Akaike (AIC) and Bayesian (BIC) 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 five representative evolutional scenarios in each of groups. Among dark energy proposal the $Λ$CDM model, CDM model with phantom field, CDM model with topological defect, model with Chaplygin gas, and the model with the linear dynamical equation of state parameter. As an alternative prototype scenarios we consider: brane world Dvali Gabadadze Porrati scenario, brane models in Randall-Sundrum scenario, Cardassian models with dust matter and radiation, 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 indicates that additional contribution arises from nonstandard 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.

astro-ph↗

arXiv2005

Cosmological model with energy transfer

The observations of SNIa suggest that we live in the acceleration epoch when the densities of the cosmological constant term and matter are almost equal. This leads to the cosmic coincidence conundrum. As the explanation for this problem we propose the FRW model with dark matter and dark energy which interact each other exchanging energy. We show that the cubic correction to the Hubble law, measured by distant supernovae type Ia, probes this interaction. We demonstrate that influences between nonrelativistic matter and vacuum sectors are controlled by third and higher derivatives of the scale factor. As an example we consider flat decaying $Λ(t)$ FRW cosmologies. We point out the possibility of measure of the energy transfer by the cubic and higher corrections to Hubble's law. The statistical analysis of SNIa data is used as an evidence of energy transfer. We find that there were the transfer from the dark energy sector to the dark matter one without any assumption about physics governing this process. We confront this hypothesis about the transfer with SNIa observations and find that the transfer the phantom and matter sector is admissible for $Ω_{\text{m},0}=0.27$. We also demonstrate that it is possible to differentiate between the energy transfer model and the variable coefficient equation of state model.

astro-ph↗

arXiv2005

Complementary constraints on non-standard cosmological models from CMB and BBN

We study metric-affine gravity (MAG) inspired cosmological models. Those models were statistically estimated using the SNIa data. We also use the cosmic microwave background observations and the big-bang nucleosynthesis analysis to constrain the density parameter $Ω_{ψ,0}$ which is related to the non-Riemannian structure of the underlying spacetime. We argue that while the models are statistically admissible from the SNIa analysis, complementary stricter limits obtained from the CMB and BBN indicate that the models with density parameters with a $a^{-6}$ scaling behaviour are virtually ruled out. If we assume the validity of the particular MAG based cosmological model throughout all stages of the Universe, the parameter estimates from the CMB and BBN put a stronger limit, in comparison to the SNIa data, on the presence of non-Riemannian structures at low redshifts.

astro-ph↗

arXiv2005

Can the initial singularity be detected by cosmological tests?

In the present paper we raise the question whether initial cosmological singularity can be proved from the cosmological tests. The classical general relativity predict the existence of singularity in the past if only some energy conditions are satisfied. On the other hand the latest quantum gravity applications to cosmology suggest of possibility of avoiding the singularity and replace it with the bounce. The distant type Ia supernovae data are used to constraints on bouncing evolutional scenario where square of the Hubble function $H^2$ is given by formulae $H^2=H^2_0[Ω_{m,0}(1+z)^{m}-Ω_{n,0}(1+z)^{n}]$, where $Ω_{m,0}, Ω_{n,0}>0$ are density parameters and $n>m>0$. We show that the on the base of the SNIa data standard bouncing models can be ruled out on the $4σ$ confidence level. If we add the cosmological constant to the standard bouncing model then we obtain as the best-fit that the parameter $Ω_{n,0}$ is equal zero which means that the SNIa data do not support the bouncing term in the model. The bounce term is statistically insignificant the present epoch. We also demonstrate that BBN offer the possibility of obtaining stringent constraints of the extra term $Ω_{n,0}$. The other observational test methods like CMB and the age of oldest objects in the Universe are used. We also use the Akaike informative criterion to select a model according to the goodness of fit and we conclude that this term should be ruled out by Occam's razor, which makes that the big bang is favored rather then bouncing scenario.

astro-ph↗

arXiv2005

Different faces of chaos in FRW models with scalar fields -- geometrical point of view

FRW cosmologies with conformally coupled scalar fields are investigated in a geometrical way by the means of geodesics of the Jacobi metric. In this model of dynamics, trajectories in the configuration space are represented by geodesics. Because of the singular nature of the Jacobi metric on the boundary set $\partial\mathcal{D}$ of the domain of admissible motion, the geodesics change the cone sectors several times (or an infinite number of times) in the neighborhood of the singular set $\partial\mathcal{D}$. We show that this singular set contains interesting information about the dynamical complexity of the model. Firstly, this set can be used as a Poincar{é} surface for construction of Poincar{é} sections, and the trajectories then have the recurrence property. We also investigate the distribution of the intersection points. Secondly, the full classification of periodic orbits in the configuration space is performed and existence of UPO is demonstrated. Our general conclusion is that, although the presented model leads to several complications, like divergence of curvature invariants as a measure of sensitive dependence on initial conditions, some global results can be obtained and some additional physical insight is gained from using the conformal Jacobi metric. We also study the complex behavior of trajectories in terms of symbolic dynamics.

gr-qc↗

arXiv2005

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

We discuss the relation between angular momenta and masses of galaxy structures base on the Li model of the universe with global rotation. In our previous paper (Godłowski et al 2002) it was shown that the model predicts the presence of a minimum in this relation. In the present paper we discuss observational evidence allowing us to verify this relation. We find null angular momentum J=0 for the masses corresponding to mass of galaxy grups and non-vanishing angular momenta for other galactic structures. We check these theoretical predictions analysing Tully's galaxy grups. The existing data comparing alignment in different galactic structure are consistent with obtained theoretical relation $J(M)$ if we interpret the groving alignment as the galactic increasing angular momenta in the galactic structure.

astro-ph↗

arXiv2004

Generalized Chaplygin Gas Models tested with SNIa

The so called Generalized Chaplygin Gas (GCG) with the equation of state $p = - \frac{A}{ρ^α}$ 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) $Ω_m= 0.3$, $Ω_{Ch}= 0.7$; (2) $Ω_m= 0.05$, $Ω_{Ch}= 0.95$ and (3) $Ω_m = 0$, $Ω_{Ch} = 1$, as well as the model withouth any assumption on $Ω_m$. The best fitted models are obtained by minimalizing the $χ^2$ function and $χ^2$ levels in the $(A_0, α)$ plane. We supplemented our analysis with confidence intervals in the $(A_0, α)$ 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 $α= 1$). Extending our analysisby relaxing the flat prior lead to the result that even though the best fitted values of $Ω_k$ 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 $Λ$CDM model high negative value of $Ω_{k}$ 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 $Λ$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 $α$ parameter and/or discriminated between GCG, Cardassian and $Λ$CDM models

astro-ph↗