Marek Demianski

Static electromagnetic geon

A static, spherically symmetric, and asymptotically flat solution of coupled Einstein-Born-Infeld equations is presented. When the internal mass of the system is zero the resulting space-time is regular and describes static electromagnetic geon.

High-redshift cosmography: new results and implications for dark energy

The explanation of the accelerated expansion of the Universe poses one of the most fundamental questions in physics and cosmology today. If the acceleration is driven by some form of dark energy (DE), and in the absence of a well-based theory to interpret the observations, one can try to constrain the parameters describing the kinematical state of the universe using a cosmographic approach, which is fundamental in that it requires only a minimal set of assumptions, namely to specify the metric, and it does not rely on the dynamical equations for gravity. Our high-redshift analysis allows us to put constraints on the cosmographic expansion up to the fifth order. It is based on the Union2 type Ia Supernovae (SNIa) data set, the Hubble diagram constructed from some gamma ray burst luminosity distance indicators, and Gaussian priors on the distance from the baryon acoustic oscillations, and the Hubble constant h (these priors have been included in order to help break the degeneracies among model parameters). To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters, we use the Markov Chain Monte Carlo method (MCMC). We finally investigate implications of our results for the DE; in particular, we focus on the parametrization of the DE equation of state (EOS). Actually, a possibility of investigating the nature of DE lies in measuring the DE EOS, w, and its time (or redshift) dependence at high accuracy. However, since w(z) is not directly accessible to measurement, reconstruction methods are needed to extract it reliably from observations. Here we investigate different models of DE, described through several parametrizations of the EOS, by comparing the cosmographic and the EOS series. The main results are as follows: (a) even if relying on a mathematical approximate assumption such as the scale factor series expansion in terms of time, cosmography can be extremely useful in assessing dynamical properties of the Universe; (b) the deceleration parameter clearly confirms the present acceleration phase; (c) the MCMC method provides stronger constraints for parameter estimation, in particular for higher order cosmographic parameters (the jerk and the snap), with respect to those presented in the literature; (d) both the estimation of the jerk and the DE parameters reflect the possibility of a deviation from the � CDM cosmological model; (e) there are indications that the DE EOS is evolving for all the parametrizations that we considered; (f) the q(z) reconstruction provided by our cosmographic analysis allows for a transient acceleration.

Accelerating universe in scalar tensor models - comparison of theoretical predictions with observations

Aims. To study the possibility of the appearance of an accelerated universe in scalar tensor cosmological models. Methods. We consider scalar tensor theories of gravity assuming that the scalar field is not minimally coupled with gravity. We use this theory to study evolution of a flat homogeneous and isotropic universe. In this case the dynamical equations can be derived form a point-like Lagrangian. We study the general properties of dynamics of this system and show that for a wide range of initial conditions such models lead in a natural way to an accelerated phase of expansion of the universe. Assuming that the point-like Lagrangian admits a Noether symmetry, we are able to explicitly solve the dynamical equations. Results. We study one particular model and show that its predictions are compatible with observational data, namely the publicly available data on type Ia supernovae, the parameters of large scale structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS), the measurements of cosmological distances with the Sunyaev-Zel’dovich effect and the rate of growth of density perturbations. This model produces in a natural way an epoch of accelerated expansion. With an appropriate choice of parameters our model is fully compatible with several observed characteristics of the universe.

Two viable quintessence models of the Universe: Confrontation of theoretical predictions with observational data

We use some of the recently released observational data to test the viability of two classes of minimally coupled scalar field models of quintessence with exponential potentials for which exact solutions of the Einstein equations are known. These models are very sturdy, depending on only one parameter - the Hubble constant. To compare predictions of our models with observations we concentrate on the following data: the power spectrum of the CMBR anisotropy as measured by WMAP, the publicly available data on type Ia supernovae, and the parameters of large scale structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS). We use the WMAP data on the age of the universe and the Hubble constant to fix the free parameters in our models. We then show that the predictions of our models are consistent with the observed positions and relative heights of the first 3 peaks in the CMB power spectrum, with the energy density of dark energy as deduced from observations of distant type Ia supernovae, and with parameters of the large scale structure as determined by 2dFGRS, in particular with the average density of dark matter. Our models are also consistent with the results of the Sloan Digital Sky Survey (SDSS). Moreover, we investigate the evolution of matter density perturbations in our quintessential models, solve exactly the evolution equation for the density perturbations, and obtain an analytical expression for the growth index f .W e verify that the approximate relation f � Ω α also holds in our models.

Standardizing the gamma‐ray bursts with the Amati Ep,i–Eiso relation: the updated Hubble diagram and implications for cosmography

The correlation between the peak photon energy of the internal spectrum Ep,i and isotropic equivalent radiated energy Eiso (the Amati relation) is explored in a scalar field model of dark energy. Using an updated data set of 109 high-redshift gamma-ray bursts (GRBs), we show that the correlation parameters only weakly depend on the cosmological model. Once the parameters of the Amati relation have been determined, we use this relation to construct a fiducial GRB Hubble diagram (HD) that extends up to redshifts ∼8. Moreover, we apply a local regression technique to estimate, in a model-independent way, the distance modulus from the recently updated Union Type Ia supernova (SNIa) sample, containing 557 SNIa spanning the redshift range of 0.015 ≤ z ≤ 1.55. The derived calibration parameters are used to construct an updated GRB HD, which we call the calibrated GRB HD. We also compare the fiducial and calibrated GRB HDs, which turned out to be fully statistically consistent, thus indicating that they are not affected by any systematic bias induced by the different calibration procedures. This means that the high-redshift GRBs can be used to test different models of dark energy settling the circularity problem. Furthermore, we investigate possible evolutionary effects that might have important influence on our results. Our analysis indicates that the presently available GRB data sets do not show statistically unambiguous evolutionary effect with the cosmological redshift. Finally, we propose another approach to calibrate the GRB relations, by using an approximate luminosity–distance relation, which holds in any cosmological model. We use this calibration of the Amati relation to construct an empirical approximate HD, which we compare with the calibrated GRB HD. We finally investigate the implications of this approach for the high-redshift cosmography.

Approximate angular diameter distance in a locally inhomogeneous universe with nonzero cosmological constant

We derive and solve exactly the Dyer-Roeder equation in a Friedman-Robertson-Walker cosmological model with non zero cosmological constant. To take into account non homogeneous distribution of matter we use the phenomenological clumpiness parameter. We propose also a general form of an approximate solution which is simple enough to be useful in practical applications and sufficiently accurate in the interesting range of redshifts.We discuss the general and approximate angular diameter distance in the Friedman-Robertson-Walker cosmological models with nonzero cosmological constant. We modify the equation for the angular diameter distance by taking into account the fact that locally the distribution of matter is non homogeneous. We present exact solutions of this equation in a few special cases. We propose an approximate analytic solution of this equation which is simple enough and sufficiently accurate to be useful in practical applications.

The GRBs Hubble diagram in quintessential cosmological models

It has been recently empirically established that some of the directly observed pa- rameters of GRBs are correlated with their important intrinsic parameters, like the luminosity or the total radiated energy. These correlations were derived, tested and used to standardize GRBs, i.e., to derive their luminosity or radiated energy from one or more observables, in order to construct an estimated fiducial Hubble diagram, assuming that radiation propagates in the standard LambdaCDM cosmological model. We extend these analyses by considering more general models of dark energy, and an updated data set of high redshift GRBs. We show that the correlation parameters only weakly depend on the cosmological model. Moreover we apply a local regression technique to estimate, in a model independent way, the distance modulus from the recently updated SNIa sample containing 307 SNIa (Astier et al. 2006), in order to calibrate the GRBs 2D correlations, considering only GRBs with z <1.4. The derived calibration parameters are used to construct a new GRBs Hubble diagram, which we call the calibrated GRBs HD. We also compare the estimated and calibrated GRBs HDs. It turns out that for the common GRBs they are fully statistically consistent, thus indicating that both of them are not affected by any systematic bias induced by the different standardizing procedures. We finally apply our methods to calibrate 95 long GRBs with the well-known Amati relation and construct the estimated and calibrated GRBs Hubble diagram that extends to redshifts z ~ 8. Even in this case there is consistency between these datasets. This means that the high redshift GRBs can be used to test different models of dark energy. We used the calibrated GRBs HD to constrain our quintessential cosmological model and derived the likelihood values of Omega_m and w(0).

Cosmological models in scalar tensor theories of gravity and observations: a class of general solutions

Aims. We study cosmological models in scalar tensor theories of gravity with power-law potentials as models of an accelerating universe. Methods. We consider cosmological models in scalar tensor theories of gravity that describe an accelerating universe and study a family of inverse power-law potentials, for which exact solutions of the Einstein equations are known. We also compare theoretical predictions of our models with observations. For this we use the following data: the publicly available catalogs of type Ia supernovae and high redshift gamma ray bursts, the parameters of large-scale structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS), and measurements of cosmological distances based on the Sunyaev-Zel’dovich effect, among others. Results. We present a class of cosmological models that describe the evolution of a homogeneous and isotropic universe filled with dust-like matter and a scalar field that is non minimally-coupled to gravity. We show that this class of models depends on three parameters: V0 – the amplitude of the scalar field potential, � H0 – the present value of the Hubble constant, and a real parameter s that determines the overall evolution of the universe. It turns out that these models have a very interesting feature naturally producing an epoch of accelerated expansion. We fix the values of these parameters by comparing predictions of our model with observational data. It turns out that our model is compatible with the presently available observational data.

A Comparison of Measured Crab and Vela Glitch Healing Parameters with Predictions of Neutron Star Models

There are currently two well-accepted models that explain how pulsars exhibit glitches, sudden changes in their regular rotational spin-down. According to the starquake model, the glitch healing parameter Q, which is measurable in some cases from pulsar timing, should be equal to the ratio of the moment of inertia of the superfluid core of a neutron star (NS) to its total moment of inertia. Measured values of the healing parameter from pulsar glitches can therefore be used in combination with realistic NS structure models as one test of the feasibility of the starquake model as a glitch mechanism. We have constructed NS models using seven representative equations of state of superdense matter to test whether starquakes can account for glitches observed in the Crab and Vela pulsars, for which the most extensive and accurate glitch data are available. We also present a compilation of all measured values of Q for Crab and Vela glitches to date that have been separately published in the literature. We have computed the fractional core moment of inertia for stellar models covering a range of NS masses and find that for stable NSs in the realistic mass range 1:4 � 0:2 M� , the fraction is greater than 0.55 in all cases. This range is not consistent with the observational restriction Qd0:2 for Vela if starquakes are the cause of its glitches. This confirms results of previous studies of the Vela pulsar that have suggested that starquakes are not a feasible mechanism for Vela glitches. The much larger values of Q observed for Crab glitches (Qe0:7) are consistent with starquake model predictions and support previous conclusions that starquakes can be the cause of Crab glitches. Subject headings: pulsars: individual (PSR B0531+21, PSR B0833� 45) — stars: neutron

Observational Estimates of the Initial Power Spectrum at Small Scale from Lyα Absorbers

We present a new method of measuring the power spectrum of initial perturbations to an unprecedentedly small scale of ~10 h-1 kpc. We apply this method to a sample of 4500 Lyα absorbers and recover the cold dark matter (CDM)-like power spectrum at scales ≥300 h-1 kpc with a precision of ~10%. However, at scales ~10-300 h-1 kpc, the measured and CDM-like spectra are noticeably different. This result suggests a complex inflation with generation of excess power at small scales. The magnitude and reliability of these deviations depend upon the possible incompleteness of our sample and poorly understood process of formation of weak absorbers. Confirmation of the CDM-like shape of the initial power spectrum or detection of its distortions at small scales are equally important for widely discussed problems of physics of the early universe, galaxy formation, and reheating of the universe. We use the Zeldovich theory of gravitational instability to derive statistical description of the properties of observed structure. Our method links the observed mass function of absorbers with the correlation function of the initial velocity field and therefore avoids the Nyquist restrictions limiting the investigations based on the smoothed flux or density fields. This approach is in general consistent with numerical simulations of the process of structure formation, describes reasonably well the large-scale structure observed in the galaxy distribution at small redshifts, and emphasizes the generic similarity of galaxies and absorbers. The physical model of absorbers adopted here asserts that they are formed in the course of both linear and nonlinear adiabatic or shock compression of dark matter (DM) and gaseous matter. It allows us to link the column density and overdensity of DM and gaseous components with observed characteristics of absorbers such as the column density of neutral hydrogen, redshifts, and Doppler parameter. At scales ≥1 h-1 Mpc, all characteristics of the DM component, and in particular, their redshift distribution, are found to be consistent with theoretical expectations for Gaussian initial perturbations with a CDM-like power spectrum.