arXiv subjects

Marek Szydlowski

Publications and source records attributed to Marek Szydlowski.

At least 73 records · Page 4Linked to original sources

arXiv2008

Coupling constant constraints in a nonminimally coupled phantom cosmology

In the paper we investigate observational constraints on coupling to gravity constant parameter $ξ$ using distant supernovae SNIa data, baryon oscillation peak (BOP), the cosmic microwave background radiation (CMBR) shift parameter, and $H(z)$ data set. We estimate the value of this parameter to constrain the extended quintessence models with nonminimally coupled to gravity phantom scalar field. The combined analysis of observational data favors a value of $ξ$ which lies in close neighborhood of the conformal coupling. While our estimations are model dependent they give rise to a indirect bound on the Equivalence Principle.

astro-ph↗

arXiv2008

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 $Λ$CDM model which is 74%. This fact is a quantitative exemplification of a turmoil in modern cosmology over the $Λ$ problem.

astro-ph↗

arXiv2007

Extended Quintessence with non-minimally coupled phantom scalar field

We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $ψ$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant. We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion that which cosmological scenario is realized depends on behavior of the system on the phase plane $(ψ, ψ')$. We formulate simple conditions on the value of coupling constant $ξ$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value $w=-1$. We describe this condition in terms of slow-roll parameters calculated at the critical point. We discover that the generic trajectories in the focus-attractor scenario come from the unstable node. It is also investigated the exact form of the parametrization of the equation of state parameter $w(z)$ (directly determined from dynamics) which assumes a different form for both scenarios.

hep-th↗

arXiv2007

Constraining bouncing cosmology caused by Casimir effect

In our paper we constrain Friedman Robertson Walker (FRW) model with ``radiation-like'' contribution to the Friedmann equation against the astronomical data. We analyze the observational limitations on a $(1+z)^4$ term from SNIa data, FRIIb radio galaxy (RG) data, baryon oscillation peak and CMBR observations. We argue that it is not possible to determine the energy densities of individual components scaling like radiation from a kinematic astronomical test. The bounds for density parameter for total radiation-like term can be obtained. We find different interpretations of the presence of scaling like radiation term: FRW universe filled with a massless scalar field in a quantum regime (Casimir effect), Friedmann-Robertson-Walker (FRW) model in a semi-classical approximation of loop quantum gravity, FRW model in the Randall Sundrum scenario with dark radiation or cosmological model with global rotation. In this paper we mainly concentrate on Casimir effect arising from quantum effects of the scalar field. This contribution can describe decaying part of cosmological constant. We discuss the back reaction of gravity on Casimir-type force which is a manifestation of the vacuum fluctuations of the quantum scalar field at low temperature. It is shown that while the Casimir energy gives rise to accelerating Universe, the cosmological constant term is still required. We argue that a small negative contribution of a radiation-like term can reconcile the tension between the observed primordial ${}^4He$ and $D$ abundance. Moreover the presence of such contribution can also remove the disagreement between Hubble parameter $H_0$ values obtained from both SNIa and Wilkinson Microwave Anisotropy Probe (WMAP) satellite data.

astro-ph↗

arXiv2007

Dissipative or Conservative cosmology with dark energy ?

All evolutional paths for all admissible initial conditions of FRW cosmological models with dissipative dust fluid (described by dark matter, baryonic matter and dark energy) are analyzed using dynamical system approach. With that approach, one is able to see how generic the class of solutions leading to the desired property -- acceleration -- is. The theory of dynamical systems also offers a possibility of investigating all possible solutions and their stability with tools of Newtonian mechanics of a particle moving in a 1-dimensional potential which is parameterized by the cosmological scale factor. We demonstrate that flat cosmology with bulk viscosity can be treated as a conservative system with a potential function of the Chaplygin gas type. We also confront viscous models with SNIa observations. The best fitted models are obtained by minimizing the $χ^{2}$ function which is illustrated by residuals and $χ^{2}$ levels in the space of model independent parameters. The general conclusion is that SNIa data supports the viscous model without the cosmological constant. The obtained values of $χ^{2}$ statistic are comparable for both the viscous model and LCDM model. The Bayesian information criteria are used to compare the models with different power law parameterization of viscous effects. Our result of this analysis shows that SNIa data supports viscous cosmology more than the LCDM model if the coefficient in viscosity parameterization is fixed. The Bayes factor is also used to obtain the posterior probability of the model.

astro-ph↗

arXiv2007

Constraints on oscillating dark energy models

The oscillating scenario of route to Lambda was recently proposed by us arXiv:0704.1651 as an alternative to a cosmological constant in a explanation of the current accelerating universe. In this scenario phantom scalar field conformally coupled to gravity drives the accelerating phase of the universe. In our model $Λ$CDM appears as a global attractor in the phase space. In this paper we investigate observational constraints on this scenario from recent measurements of distant supernovae type Ia, CMB R shift, BAO and $H(z)$ observational data. The Bayesian methods of model selection are used in comparison the model with concordance $Λ$CDM one as well as with model with dynamical dark energy parametrised by linear form. We conclude that $Λ$CDM is favoured over FRW model with dynamical oscillating dark energy. Our analysis also demonstrate that FRW model with oscillating dark energy is favoured over FRW model with decaying dark energy parametrised in linear way.

astro-ph↗

arXiv2007

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.

astro-ph↗

arXiv2007

Relic gravitons from super-inflation

The super-inflationary phase is predicted by the Loop Quantum Cosmology. In this paper we study the creation of gravitational waves during this phase. We consider the inverse volume corrections to the equation for the tensor modes and calculate the spectrum of the produced gravitons. The amplitude of the obtained spectrum as well as maximal energy of gravitons strongly depend on the evolution of the Universe after the super-inflation. We show that a further standard inflationary phase is necessary to lower the amount of gravitons below the present bound. In case of the lack of the standard inflationary phase, the present intensity of gravitons would be extremely large. These considerations give us another motivation to introduce the standard phase of inflation.

gr-qc↗

arXiv2007

Relic gravitons as the observable for Loop Quantum Cosmology

In this paper we investigate tensor modes of perturbations in the universe governed by Loop Quantum Cosmology. We derive the equation for tensor modes and investigate numerically effects of quantum corrections. This investigation reveals that the region of super-adiabatic amplification of tensor modes is smaller in comparison with the classical case. Neglecting quantum corrections to the equation for tensor modes and holding underlying loop dynamics we study analytically the creation of gravitons. We calculate the power spectrum of tensor perturbations during the super-inflationary phase induced by Loop Quantum Gravity. The main result obtained is the spectrum of gravitons, produced in the transition from the quantum to classical regime of the Universe. Obtained spectrum is characterized by a hard branch. The numerical investigation shows the strong dependence of $ν_{\text{max}}$ frequency with respect to quantum numbers. The parameter $Ω_{\text{gw}}(ν_{\text{max}})$ approaches even to $\sim 10^{-1}$ for highest frequencies. We compare our results with recent constraints from the Laser Interferometer Gravitational-wave Observatory (LIGO) and find that it is possible to test the quantum effects in the early Universe.

gr-qc↗

arXiv2007

Route to Lambda in conformally coupled phantom cosmology

In this letter we investigate acceleration in the flat cosmological model with a conformally coupled phantom field and we show that acceleration is its generic feature. We reduce the dynamics of the model to a 3-dimensional dynamical system and analyze it on a invariant 2-dimensional submanifold. Then the concordance FRW model with the cosmological constant $Λ$ is a global attractor situated on a 2-dimensional invariant space. We also study the behaviour near this attractor, which can be approximated by the dynamics of the linearized part of the system. We demonstrate that trajectories of the conformally coupled phantom scalar field with a simple quadratic potential crosses the cosmological constant barrier infinitely many times in the phase space. The universal behaviour of the scalar field and its potential is also calculated. We conclude that the phantom scalar field conformally coupled to gravity gives a natural dynamical mechanism of concentration of the equation of state coefficient around the magical value $w_{\text{eff}}=-1$. We demonstrate route to Lambda through the infinite times crossing the $w_{\text{eff}}=-1$ phantom divide.

hep-th↗

arXiv2007

Phantom cosmology as a scattering process

We study the general chaotic features of dynamics of the phantom field modelled in terms of a single scalar field conformally coupled to gravity. We demonstrate that the dynamics of the FRW model with dark energy in the form of phantom field can be regarded as a scattering process of two types: multiple chaotic and classical non-chaotic. It depends whether the spontaneously symmetry breaking takes place. In the first class of models with the spontaneously symmetry breaking the dynamics is similar to the Yang-Mills theory. We find the evidence of a fractal structure in the phase space of initial conditions. We observe similarities to the phenomenon of a multiple scattering process around the origin. In turn the class of models without the spontaneously symmetry breaking can be described as the classical non-chaotic scattering process and the methods of symbolic dynamic are also used in this case. We show that the phantom cosmology can be treated as a simple model with scattering of trajectories which character depends crucially on a sign of a square of mass. We demonstrate that there is a possibility of chaotic behavior in the flat Universe with a conformally coupled phantom field in the system considered on non-zero energy level. We obtain that the acceleration is a generic feature in the considered model without the spontaneously symmetry breaking. We observe that the effective EOS coefficient oscillates and then approach to $w=-1$.

hep-th↗

arXiv2007

Acceleration of the Universe driven by the Casimir force

We investigate an evolutional scenario of the FRW universe with the Casimir energy scaling like $(-)(1+z)^4$. The Casimir effect is used to explain the vacuum energy differences (its value measured from astrophysics is so small compared to value obtained from quantum field theory calculations). The dynamics of the FRW model is represented in terms of a two-dimensional dynamical system to show all evolutional paths of this model in the phase space for all admissible initial conditions. We find also an exact solution for non flat evolutional paths of Universe driven by the Casimir effect. The main difference between the FRW model with the Casimir force and the $Λ$CDM model is that their generic solutions are a set of evolutional paths with a bounce solution and an initial singularity, respectively. The evolutional scenario are tested by using the SNIa data, FRIIb radiogalaxies, baryon oscillation peak and CMB observation. We compare the power of explanation of the model considered and the $Λ$CDM model using the Bayesian information criterion and Bayesian factor. Our investigation of the information criteria of model selection showed the preference of the $Λ$CDM model over the model considered. However the presence of negative like the radiation term can remove a tension between the theoretical and observed primordial ${}^4$He and D abundance.

gr-qc↗

arXiv2007

Global dynamics of cosmological scalar fields -- Part II

This is the second part of integrability analysis of cosmological models with scalar fields. Here, we study systems with conformal coupling, and show that apart from four cases, where explicit first integrals are known, the generic system is not integrable. We also comment on some chaotic properties of the system, and the issues of integrability restricted to the real domain.

gr-qc↗

arXiv2007

Exact solutions in bouncing cosmology

We discuss the effects of a (possibly) negative $(1+z)^6$ type contribution to the Friedmann equation. No definite answer can be given as to the presence and magnitude of a particular mechanism, because any test using the general relation $H(z)$ is able to estimate only the total of all sources of such a term. That is why we describe four possibilities: 1) geometric effects of loop quantum cosmology, 2) braneworld cosmology, 3) metric-affine gravity, and 4) cosmology with spinning fluid. We find the exact solutions for the models with $ρ^2$ correction in terms of elementary functions, and show all evolutional paths on their phase plane. Instead of the initial singularity, the generic feature is now a bounce.

gr-qc↗

arXiv2006

Global dynamics of cosmological scalar fields -- Part I

We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as introduced by Morales-Ruiz and Ramis. The main result is that the generic systems are non-integrable, although there still exist some values of parameters for which integrability remains undecided. We also draw a connection with chaos present in such cosmological models. The first part of the article deals with minimally coupled fields, and the second treats the conformal couping.

gr-qc↗

arXiv2006

Towards observational constraints on negative (1+z)^4 type contribution in the Friedmann equation

We discuss certain issues related to the limitations of density parameters for a ``radiation''-like contribution to the Friedmann equation using kinematical or geometrical measurements. We analyse the observational constraint of a negative $(1+z)^4$-type contribution in cosmological models. We argue that it is not possible to determine the energy densities of individual components of matter scaling like radiation from astronomical observations. We find three different interpretations of the presence of the radiation term: 1) the FRW universe filled with a massless scalar field in a quantum regime (the Casimir effect), 2) the Friedmann-Robertson-Walker (FRW) model in the Randall Sundrum scenario with dark radiation, 3) the cosmological model with global rotation. From supernovae type Ia (SNIa) data, Fanaroff-Riley type IIb (FRIIb) radio galaxy (RG) data, baryon oscillation peak and cosmic microwave background radiation (CMBR) observations we obtain bounds for the negative radiation-like term. A small negative contribution of dark radiation can reconcile the tension in nucleosynthesis and remove also the disagreement between $H_0$ values obtained from both SNIa and the Wilkinson Microwave Anisotropy Probe (WMAP) satellite data.

astro-ph↗

arXiv2006

Cosmological zoo -- accelerating models with dark energy

ecent observations of type Ia supernovae indicate that the Universe is in an accelerating phase of expansion. The fundamental quest in theoretical cosmology is to identify the origin of this phenomenon. In principle there are two possibilities: 1) the presence of matter which violates the strong energy condition (a substantial form of dark energy), 2) modified Friedmann equations (Cardassian models -- a non-substantial form of dark matter). We classify all these models in terms of 2-dimensional dynamical systems of the Newtonian type. We search for generic properties of the models. It is achieved with the help of Peixoto's theorem for dynamical system on the Poincar{é} sphere. We find that the notion of structural stability can be useful to distinguish the generic cases of evolutional paths with acceleration. We find that, while the $Λ$CDM models and phantom models are typical accelerating models, the cosmological models with bouncing phase are non-generic in the space of all planar dynamical systems. We derive the universal shape of potential function which gives rise to presently accelerating models. Our results show explicitly the advantages of using a potential function (instead of the equation of state) to probe the origin of the present acceleration. We argue that simplicity and genericity are the best guide in understanding our Universe and its acceleration.

astro-ph↗

arXiv2006

Dynamical dark energy models -- dynamical system approach

We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state $p_{x}=w_{x}(a(z)) ρ_{x}$ in which the coefficient $w_{x}$ is parameterized by the scale factor $a$ or redshift $z$. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential $V(a)$. One of the features of this reduction is the possibility of investigating how typical are big rip singularities in the future evolution of the model. The properties of potential function $V$ can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.

gr-qc↗