Cosmology with gamma-ray bursts: I. The Hubble diagram through the calibrated Ep,iE_{\rm p,i} - EisoE_{\rm iso} correlation

Gamma-ray bursts are the most energetic explosions in the Universe. They are detectable up to very high redshifts, therefore can be used to study the expansion rate of the Universe and to investigate the observational properties of dark energy, provided that empirical correlations between spectral and intensity properties are appropriately calibrated. We used the type Ia supernova luminosity distances to calibrate the correlation between the peak photon energy, $E_{p, i}$, and the isotropic equivalent radiated energy, $E_{iso}$ in GRBs. With this correlation, we tested the reliability of applying GRBs to measure cosmological parameters and to obtain indications on the basic properties and evolution of dark energy. Using 162 GRBs with measured redshifts and spectra, we applied a local regression technique to calibrate the $E_{p, i}$-$E_{iso}$ correlation against the type Ia SN data to build a calibrated GRB Hubble diagram. We tested the possible redshift dependence of the correlation and its effect on the Hubble diagram. Finally, we used the GRB Hubble diagram to investigate the dark energy EOS. For this, we focused on the so-called Chevalier-Polarski-Linder (CPL) parametrization of the dark energy EOS and implemented the Markov chain Monte Carlo (MCMC) method to efficiently sample the space of cosmological parameters. Our analysis shows once more that the $E_{p, i}$-$E_{iso}$ correlation has no significant redshift dependence. Therefore the high-redshift GRBs can be used as a cosmological tool to determine the basic cosmological parameters and to test different models of dark energy in the redshift region ($z\geqslant 3$), which is unexplored by the SNIa and baryonic acoustic oscillations data. Our updated calibrated Hubble diagram of GRBs provides some marginal indication (at $1\sigma$ level) of an evolving dark energy EOS.Comment: 12 pages, 11 figure

Why not a di-NUT? or Gravitational duality and rotating solutions

We study how gravitational duality acts on rotating solutions, using the Kerr-NUT black hole as an example. After properly reconsidering how to take into account both electric (i.e. mass-like) and magnetic (i.e. NUT-like) sources in the equations of general relativity, we propose a set of definitions for the dual Lorentz charges. We then show that the Kerr-NUT solution has non-trivial such charges. Further, we clarify in which respect Kerr's source can be seen as a mass M with a dipole of NUT charges.Comment: 20 pages. v2: minor clarifications in section 4, version to appear in PR

Standardizing the GRBs 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 GRBs, we show that the correlation parameters only weakly depend on the cosmological model. Once the parameters of Amati relation have been determined we use this relation to construct a fiducial GRBs Hubble diagram 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 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 GRBs Hubble diagram, which we call the calibrated GRBs HD. We also compare the fiducial and calibrated GRBs 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 GRBs datasets 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 GRBs HD. We finally investigate the implications of this approach for the high redshift cosmography.Comment: 18 figures and 1 table, accepted for publication on MNRA

Statistical characteristics of observed Ly-α\alpha forest and the shape of linear power spectrum

Properties of $\sim$ 6 000 Ly-$\alpha$ absorbers observed in 19 high resolution spectra of QSOs are investigated using the model of formation and evolution of DM structure elements based on the Zel'dovich theory. This model asserts that absorbers 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 the observed column density of neutral hydrogen, redshifts and Doppler parameters of absorbers and demonstrates that at high redshifts we observe a self similar period of structure evolution with the Gaussian initial perturbations. We show that the colder absorbers are associated with rapidly expanded regions of a galactic scale which represent large amplitude negative density perturbations. We extend and improve the method of measuring the power spectrum of initial perturbations proposed in Demia\'nski & Doroshkevich (2003b). Our method links the observed separations and the DM column density of absorbers with the correlation function of the initial velocity field. We recover the cold dark matter (CDM) like power spectrum at scales 10> D > 0.15Mpc/h with a precision of ~15%. However at scales $\sim 3 - 150 h^{-1}$kpc the measured and CDM--like spectra are different. This result suggests a possible complex inflation with generation of excess power at small scales.Comment: 21 pages, 7 figures, MNRAS submitte

Cosmology with gamma-ray bursts: II Cosmography challenges and cosmological scenarios for the accelerated Universe

Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that the space time ge- ometry is described by the Friedman-Lemaitre-Robertson-Walker metric, and adopting an approach that effectively uses only Taylor expansions of basic observables. Aims. We perform a high-redshift analysis to constrain the cosmographic expansion up to the fifth order. It is based on the Union2 type Ia supernovae data set, the gamma-ray burst Hubble diagram, a data set of 28 independent measurements of the Hubble param- eter, baryon acoustic oscillations measurements from galaxy clustering and the Lyman-{\alpha} forest in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), and some Gaussian priors on h and {\Omega}M . Methods. We performed a statistical analysis and explored the probability distributions of the cosmographic parameters. By building up their regions of confidence, we maximized our likelihood function using the Markov chain Monte Carlo method. Results. Our high-redshift analysis confirms that the expansion of the Universe currently accelerates; the estimation of the jerk parameter indicates a possible deviation from the standard {\Lambda}CDM cosmological model. Moreover, we investigate implications of our results for the reconstruction of the dark energy equation of state (EOS) by comparing the standard technique of cosmography with an alternative approach based on generalized Pad\'e approximations of the same observables. Because these expansions converge better, is possible to improve the constraints on the cosmographic parameters and also on the dark matter EOS. Conclusions. The estimation of the jerk and the DE parameters indicates at 1{\sigma} a possible deviation from the {\Lambda}CDM cosmological model.Comment: 10 pages, 7 figures, accepted for publication in A &

Redshift distribution of {\bf Ly-α\alpha} lines and metal systems

The observed redshift distribution of Ly-$\alpha$ lines and metal systems is examined in order to discriminate and to trace the evolution of structure elements observed in the galaxy distribution, at small redshifts, and to test the theoretical description of structure evolution. We show that the expected evolution of filamentary component of structure describes quite well the redshift distribution of metal systems and stronger Ly-$\alpha$ lines with $\log(N_{HI})\geq$14, at $z\leq$ 3. The redshift distribution of weaker Ly-$\alpha$ lines can be attributed to the population of poorer structure elements (Zel'dovich pancakes), which were formed at high redshifts from the invisible DM and non luminous baryonic matter, and at lower redshifts they mainly merged and dispersed.Comment: 13 pages, 5 figures, accepted in MNRA

A stationary vacuum solution dual to the Kerr solution

We present a stationary axially symmetric two parameter vacuum solution which could be considered as ``dual'' to the Kerr solution. It is obtained by removing the mass parameter from the function of the radial coordinate and introducing a dimensionless parameter in the function of the angle coordinate in the metric functions. It turns out that it is in fact the massless limit of the Kerr - NUT solution.Comment: Latex, 4 pages, minor modifications in title and discussion. Accepted in Mod. Phys. Lett.

Einstein-Born-Infeld on Taub-NUT Spacetime in 2k+2 Dimensions

We wish to construct solutions of Taub-NUT spacetime in Einstein-Born-Infeld gravity in even dimensions. Since Born-Infeld theory is a nonlinear electrodynamics theory, in leads to nonlinear differential equations. However a proper analytical solution was not obtain, we try to solve it numerically (by the Runge-Kotta method) with initial conditions coinciding with those of our previous work in Einstein-Maxwell gravity. We solve equations for 4, 6 and 8 dimensions and do data fitting by the least-squares method. For N=l=b=1, the metric turns to the NUT solution only in 8 dimensions, but in 4 and 6 dimensions the spacetime does not have any Nut solution.Comment: 8 pages, 5 figure