Cosmological Constraints from calibrated Yonetoku and Amati relation implies Fundamental plane of Gamma-ray bursts

We consider two empirical relations using data only from the prompt emission of Gamma-Ray Bursts (GRBs), peak energy ($E_p$) - peak luminosity ($L_p$) relation (so called Yonetoku relation) and $E_p$-isotropic energy ($E_{\rm iso}$) relation (so called Amati relation). We first suggest the independence of the two relations although they have been considered similar and dependent. From this viewpoint, we compare constraints on cosmological parameters, $\Omega_m$ and $\Omega_{\Lambda}$, from the Yonetoku and Amati relations calibrated by low-redshift GRBs with $z < 1.8$. We found that they are different in 1-$\sigma$ level, although they are still consistent in 2-$\sigma$ level. This and the fact that both Amati and Yonetoku relations have systematic errors larger than statistical errors suggest the existence of a hidden parameter of GRBs. We introduce the luminosity time $T_L$ defined by $T_L\equiv E_{\rm iso}/L_p$ as a hidden parameter to obtain a generalized Yonetoku relation as $(L_p/{10^{52} \rm{erg s^{-1}}}) = 10^{-3.88\pm0.09}(E_p/{\rm{keV}})^{1.84\pm0.04} (T_L/{\rm{s}})^{-0.34\pm0.04}$. The new relation has much smaller systematic error, 30%, and can be regarded as "Fundamental plane" of GRBs. We show a possible radiation model for this new relation. Finally we apply the new relation for high-redshift GRBs with $1.8 < z < 5.6$ to obtain $(\Omega_m,\Omega_{\Lambda}) = (0.16^{+0.04}_{-0.06},1.20^{+0.03}_{-0.09})$, which is consistent with the concordance cosmological model within 2-$\sigma$ level.Comment: 5 pages, 6 figures, published in JCA

Probing the cosmic acceleration from combinations of different data sets

We examine in some detail the influence of the systematics in different data sets including type Ia supernova sample, baryon acoustic oscillation data and the cosmic microwave background information on the fitting results of the Chevallier-Polarski-Linder parametrization. We find that the systematics in the data sets does influence the fitting results and leads to different evolutional behavior of dark energy. To check the versatility of Chevallier-Polarski-Linder parametrization, we also perform the analysis on the Wetterich parametrization of dark energy. The results show that both the parametrization of dark energy and the systematics in data sets influence the evolutional behavior of dark energy.Comment: 15 pages, 5 figures and 1 table, major revision, delete bao a data, main results unchanged. jcap in press

Cosmological Model-independent Gamma-ray Bursts Calibration and its Cosmological Constraint to Dark Energy

As so far, the redshift of Gamma-ray bursts (GRBs) can extend to $z\sim 8$ which makes it as a complementary probe of dark energy to supernova Ia (SN Ia). However, the calibration of GRBs is still a big challenge when they are used to constrain cosmological models. Though, the absolute magnitude of GRBs is still unknown, the slopes of GRBs correlations can be used as a useful constraint to dark energy in a completely cosmological model independent way. In this paper, we follow Wang's model-independent distance measurement method and calculate their values by using 109 GRBs events via the so-called Amati relation. Then, we use the obtained model-independent distances to constrain $\Lambda$CDM model as an example.Comment: 16 pages, 5 figure

Observational constraint on dynamical evolution of dark energy

We use the Constitution supernova, the baryon acoustic oscillation, the cosmic microwave background, and the Hubble parameter data to analyze the evolution property of dark energy. We obtain different results when we fit different baryon acoustic oscillation data combined with the Constitution supernova data to the Chevallier-Polarski-Linder model. We find that the difference stems from the different values of $\Omega_{m0}$. We also fit the observational data to the model independent piecewise constant parametrization. Four redshift bins with boundaries at $z=0.22$, 0.53, 0.85 and 1.8 were chosen for the piecewise constant parametrization of the equation of state parameter $w(z)$ of dark energy. We find no significant evidence for evolving $w(z)$. With the addition of the Hubble parameter, the constraint on the equation of state parameter at high redshift isimproved by 70%. The marginalization of the nuisance parameter connected to the supernova distance modulus is discussed.Comment: revtex, 16 pages, 5 figures, V2: published versio

Constraints on growth index parameters from current and future observations

We use current and future simulated data of the growth rate of large scale structure in combination with data from supernova, BAO, and CMB surface measurements, in order to put constraints on the growth index parameters. We use a recently proposed parameterization of the growth index that interpolates between a constant value at high redshifts and a form that accounts for redshift dependencies at small redshifts. We also suggest here another exponential parameterization with a similar behaviour. The redshift dependent parametrizations provide a sub-percent precision level to the numerical growth function, for the full redshift range. Using these redshift parameterizations or a constant growth index, we find that current available data from galaxy redshift distortions and Lyman-alpha forests is unable to put significant constraints on any of the growth parameters. For example both $\Lambda$CDM and flat DGP are allowed by current growth data. We use an MCMC analysis to study constraints from future growth data, and simulate pessimistic and moderate scenarios for the uncertainties. In both scenarios, the redshift parameterizations discussed are able to provide significant constraints and rule out models when incorrectly assumed in the analysis. The values taken by the constant part of the parameterizations as well as the redshift slopes are all found to significantly rule out an incorrect background. We also find that, for our pessimistic scenario, an assumed constant growth index over the full redshift range is unable to rule out incorrect models in all cases. This is due to the fact that the slope acts as a second discriminator at smaller redshifts and therefore provide a significant test to identify the underlying gravity theory.Comment: 13 pages, 5 figures, matches JCAP accepted versio

From cosmic deceleration to acceleration: new constraints from SN Ia and BAO/CMB

We use type Ia supernovae (SN Ia) data in combination with recent baryonic acoustic oscillations (BAO) and cosmic microwave background (CMB) observations to constrain a kink-like parametrization of the deceleration parameter ($q$). This $q$-parametrization can be written in terms of the initial ($q_i$) and present ($q_0$) values of the deceleration parameter, the redshift of the cosmic transition from deceleration to acceleration ($z_t$) and the redshift width of such transition ($\tau$). By assuming a flat space geometry, $q_i=1/2$ and adopting a likelihood approach to deal with the SN Ia data we obtain, at the 68% confidence level (C.L.), that: $z_t=0.56^{+0.13}_{-0.10}$, $\tau=0.47^{+0.16}_{-0.20}$ and $q_0=-0.31^{+0.11}_{-0.11}$ when we combine BAO/CMB observations with SN Ia data processed with the MLCS2k2 light-curve fitter. When in this combination we use the SALT2 fitter we get instead, at the same C.L.: $z_t=0.64^{+0.13}_{-0.07}$, $\tau=0.36^{+0.11}_{-0.17}$ and $q_0=-0.53^{+0.17}_{-0.13}$. Our results indicate, with a quite general and model independent approach, that MLCS2k2 favors Dvali-Gabadadze-Porrati-like cosmological models, while SALT2 favors $\Lambda$CDM-like ones. Progress in determining the transition redshift and/or the present value of the deceleration parameter depends crucially on solving the issue of the difference obtained when using these two light-curve fitters.Comment: 25 pages, 9 figure

Observational Constraints to Ricci Dark Energy Model by Using: SN, BAO, OHD, fgas Data Sets

In this paper, we perform a global constraint on the Ricci dark energy model with both the flat case and the non-flat case, using the Markov Chain Monte Carlo (MCMC) method and the combined observational data from the cluster X-ray gas mass fraction, Supernovae of type Ia (397), baryon acoustic oscillations, current Cosmic Microwave Background, and the observational Hubble function. In the flat model, we obtain the best fit values of the parameters in $1\sigma, 2\sigma$ regions: $\Omega_{m0}=0.2927^{+0.0420 +0.0542}_{-0.0323 -0.0388}$, $\alpha=0.3823^{+0.0331 +0.0415}_{-0.0418 -0.0541}$, $Age/Gyr=13.48^{+0.13 +0.17}_{-0.16 -0.21}$, $H_0=69.09^{+2.56 +3.09}_{-2.37 -3.39}$. In the non-flat model, the best fit parameters are found in $1\sigma, 2\sigma$ regions:$\Omega_{m0}=0.3003^{+0.0367 +0.0429}_{-0.0371 -0.0423}$, $\alpha=0.3845^{+0.0386 +0.0521}_{-0.0474 -0.0523}$, $\Omega_k=0.0240^{+0.0109 +0.0133}_{-0.0130 -0.0153}$, $Age/Gyr=12.54^{+0.51 +0.65}_{-0.37 -0.49}$, $H_0=72.89^{+3.31 +3.88}_{-3.05 -3.72}$. Compared to the constraint results in the $\Lambda \textmd{CDM}$ model by using the same datasets, it is shown that the current combined datasets prefer the $\Lambda \textmd{CDM}$ model to the Ricci dark energy model.Comment: 12 pages, 3 figure

Tomography from the Next Generation of Cosmic Shear Experiments for Viable f(R) Models

We present the cosmic shear signal predicted by two viable cosmological models in the framework of modified-action f(R) theories. We use f(R) models where the current accelerated expansion of the Universe is a direct consequence of the modified gravitational Lagrangian rather than Dark Energy (DE), either in the form of vacuum energy/cosmological constant or of a dynamical scalar field (e.g. quintessence). We choose Starobinsky's (St) and Hu & Sawicki's (HS) f(R) models, which are carefully designed to pass the Solar System gravity tests. In order to further support - or rule out - f(R) theories as alternative candidates to the DE hypothesis, we exploit the power of weak gravitational lensing, specifically of cosmic shear. We calculate the tomographic shear matrix as it would be measured by the upcoming ESA Cosmic Vision Euclid satellite. We find that in the St model the cosmic shear signal is almost completely degenerate with LCDM, but it is easily distinguishable in the HS model. Moreover, we compute the corresponding Fisher matrix for both the St and HS models, thus obtaining forecasts for their cosmological parameters. Finally, we show that the Bayes factor for cosmic shear will definitely favour the HS model over LCDM if Euclid measures a value larger than ~0.02 for the extra HS parameter n_HS.Comment: 26 pages, 6 figures, 2 tables; tomographic and Bayesian analyses updated and modified according to reviewer's suggestions; references update

Consistency of LCDM with Geometric and Dynamical Probes

The LCDM cosmological model assumes the existence of a small cosmological constant in order to explain the observed accelerating cosmic expansion. Despite the dramatic improvement of the quality of cosmological data during the last decade it remains the simplest model that fits remarkably well (almost) all cosmological observations. In this talk I review the increasingly successful fits provided by LCDM on recent geometric probe data of the cosmic expansion. I also briefly discuss some emerging shortcomings of the model in attempting to fit specific classes of data (eg cosmic velocity dipole flows and cluster halo profiles). Finally, I summarize recent results on the theoretically predicted matter overdensity ($\delta_m=\frac{\delta \rho_m}{\rho_m}$) evolution (a dynamical probe of the cosmic expansion), emphasizing its scale and gauge dependence on large cosmological scales in the context of general relativity. A new scale dependent parametrization which describes accurately the growth rate of perturbations even on scales larger than 100h^{-1}Mpc is shown to be a straightforward generalization of the well known scale independent parametrization f(a)=\omms(a)^\gamma valid on smaller cosmological scales.Comment: 20 pages, 6 figures. Invited review at the 1st Mediterranean Conference on Classical and Quantum Gravity (MCCQG). To appear in the proceeding

Comparison of Recent SnIa datasets

We rank the six latest Type Ia supernova (SnIa) datasets (Constitution (C), Union (U), ESSENCE (Davis) (E), Gold06 (G), SNLS 1yr (S) and SDSS-II (D)) in the context of the Chevalier-Polarski-Linder (CPL) parametrization $w(a)=w_0+w_1 (1-a)$, according to their Figure of Merit (FoM), their consistency with the cosmological constant ($\Lambda$CDM), their consistency with standard rulers (Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO)) and their mutual consistency. We find a significant improvement of the FoM (defined as the inverse area of the 95.4% parameter contour) with the number of SnIa of these datasets ((C) highest FoM, (U), (G), (D), (E), (S) lowest FoM). Standard rulers (CMB+BAO) have a better FoM by about a factor of 3, compared to the highest FoM SnIa dataset (C). We also find that the ranking sequence based on consistency with $\Lambda$CDM is identical with the corresponding ranking based on consistency with standard rulers ((S) most consistent, (D), (C), (E), (U), (G) least consistent). The ranking sequence of the datasets however changes when we consider the consistency with an expansion history corresponding to evolving dark energy $(w_0,w_1)=(-1.4,2)$ crossing the phantom divide line $w=-1$ (it is practically reversed to (G), (U), (E), (S), (D), (C)). The SALT2 and MLCS2k2 fitters are also compared and some peculiar features of the SDSS-II dataset when standardized with the MLCS2k2 fitter are pointed out. Finally, we construct a statistic to estimate the internal consistency of a collection of SnIa datasets. We find that even though there is good consistency among most samples taken from the above datasets, this consistency decreases significantly when the Gold06 (G) dataset is included in the sample.Comment: 13 pages, 9 figures. Included recently released SDSS-II dataset. Improved presentation. Main results unchanged. The mathematica files and datasets used for the production of the figures may be downloaded from http://leandros.physics.uoi.gr/datacomp