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

High-Redshift Cosmography

We constrain the parameters describing the kinematical state of the universe using a cosmographic approach, which is fundamental in that it requires a very minimal set of assumptions (namely to specify a metric) and does not rely on the dynamical equations for gravity. On the data side, we consider the most recent compilations of Supernovae and Gamma Ray Bursts catalogues. This allows to further extend the cosmographic fit up to $z = 6.6$, i.e. up to redshift for which one could start to resolve the low z degeneracy among competing cosmological models. In order to reliably control the cosmographic approach at high redshifts, we adopt the expansion in the improved parameter $y = z/(1+z)$. This series has the great advantage to hold also for $z > 1$ and hence it is the appropriate tool for handling data including non-nearby distance indicators. We find that Gamma Ray Bursts, probing higher redshifts than Supernovae, have constraining power and do require (and statistically allow) a cosmographic expansion at higher order than Supernovae alone. Exploiting the set of data from Union and GRBs catalogues, we show (for the first time in a purely cosmographic approach parametrized by deceleration $q_0$, jerk $j_0$, snap $s_0$) a definitively negative deceleration parameter $q_0$ up to the 3$\sigma$ confidence level. We present also forecasts for realistic data sets that are likely to be obtained in the next few years.Comment: 16 pages, 6 figures, 3 tables. Improved version matching the published one, additional comments and reference

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

A Search for Ultra-High Energy Counterparts to Gamma-Ray Bursts

A small air shower array operating over many years has been used to search for ultra-high energy (UHE) gamma radiation ($\geq 50$ TeV) associated with gamma-ray bursts (GRBs) detected by the BATSE instrument on the Compton Gamma-Ray Observatory (CGRO). Upper limits for a one minute interval after each burst are presented for seven GRBs located with zenith angles $\theta < 20^{\circ}$. A $4.3\sigma$ excess over background was observed between 10 and 20 minutes following the onset of a GRB on 11 May 1991. The confidence level that this is due to a real effect and not a background fluctuation is 99.8\%. If this effect is real then cosmological models are excluded for this burst because of absorption of UHE gamma rays by the intergalactic radiation fields.Comment: 4 pages LaTeX with one postscript figure. This version does not use kluwer.sty and will allow automatic postscript generatio

Cosmological Models and Latest Observational Data

In this note, we consider the observational constraints on some cosmological models by using the 307 Union type Ia supernovae (SNIa), the 32 calibrated Gamma-Ray Bursts (GRBs) at $z>1.4$, the updated shift parameter $R$ from WMAP 5-year data (WMAP5), and the distance parameter $A$ of the measurement of the baryon acoustic oscillation (BAO) peak in the distribution of SDSS luminous red galaxies with the updated scalar spectral index $n_s$ from WMAP5. The tighter constraints obtained here update the ones obtained previously in the literature.Comment: 10 pages, 5 figures, 1 table, revtex4; v2: discussions added, accepted by Eur. Phys. J. C; v3: published versio

Early Dark Energy at High Redshifts: Status and Perspectives

Early dark energy models, for which the contribution to the dark energy density at high redshifts is not negligible, influence the growth of cosmic structures and could leave observable signatures that are different from the standard cosmological constant cold dark matter ($\Lambda$CDM) model. In this paper, we present updated constraints on early dark energy using geometrical and dynamical probes. From WMAP five-year data, baryon acoustic oscillations and type Ia supernovae luminosity distances, we obtain an upper limit of the dark energy density at the last scattering surface (lss), $\Omega_{\rm EDE}(z_{\rm lss})<2.3\times10^{-2}$ (95% C.L.). When we include higher redshift observational probes, such as measurements of the linear growth factors, Gamma-Ray Bursts (GRBs) and Lyman-$\alpha$ forest (\lya), this limit improves significantly and becomes $\Omega_{\rm EDE}(z_{\rm lss})<1.4\times10^{-3}$ (95% C.L.). Furthermore, we find that future measurements, based on the Alcock-Paczy\'nski test using the 21cm neutral hydrogen line, on GRBs and on the \lya forest, could constrain the behavior of the dark energy component and distinguish at a high confidence level between early dark energy models and pure $\Lambda$CDM. In this case, the constraints on the amount of early dark energy at the last scattering surface improve by a factor ten, when compared to present constraints. We also discuss the impact on the parameter $\gamma$, the growth rate index, which describes the growth of structures in standard and in modified gravity models.Comment: 11 pages, 9 figures and 4 table

On the true nature of renormalizability in Horava-Lifshitz gravity

We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.Comment: Latex file in Revtex style, 5 pages, no figures. v2: references added, version accepted for publication in Foundations of Physic

Observational Constraints on Cosmological Models with the Updated Long Gamma-Ray Bursts

In the present work, by the help of the newly released Union2 compilation which consists of 557 Type Ia supernovae (SNIa), we calibrate 109 long Gamma-Ray Bursts (GRBs) with the well-known Amati relation, using the cosmology-independent calibration method proposed by Liang {\it et al.}. We have obtained 59 calibrated high-redshift GRBs which can be used to constrain cosmological models without the circularity problem (we call them ``Hymnium'' GRBs sample for convenience). Then, we consider the joint constraints on 7 cosmological models from the latest observational data, namely, the combination of 557 Union2 SNIa dataset, 59 calibrated Hymnium GRBs dataset (obtained in this work), the shift parameter $R$ from the WMAP 7-year data, and the distance parameter $A$ of the measurement of the baryon acoustic oscillation (BAO) peak in the distribution of SDSS luminous red galaxies. We also briefly consider the comparison of these 7 cosmological models.Comment: 19 pages, 3 tables, 10 figures, revtex4; v2: accepted for publication in JCAP; v3: published versio

Time of arrival through interacting environments: Tunneling processes

We discuss the propagation of wave packets through interacting environments. Such environments generally modify the dispersion relation or shape of the wave function. To study such effects in detail, we define the distribution function P_{X}(T), which describes the arrival time T of a packet at a detector located at point X. We calculate P_{X}(T) for wave packets traveling through a tunneling barrier and find that our results actually explain recent experiments. We compare our results with Nelson's stochastic interpretation of quantum mechanics and resolve a paradox previously apparent in Nelson's viewpoint about the tunneling time.Comment: Latex 19 pages, 11 eps figures, title modified, comments and references added, final versio

Gamma Ray Bursts as Probes of Quantum Gravity

Gamma ray bursts (GRBs) are short and intense pulses of $\gamma$-rays arriving from random directions in the sky. Several years ago Amelino-Camelia et al. pointed out that a comparison of time of arrival of photons at different energies from a GRB could be used to measure (or obtain a limit on) possible deviations from a constant speed of light at high photons energies. I review here our current understanding of GRBs and reconsider the possibility of performing these observations.Comment: Lectures given at the 40th winter school of theretical physics: Quantum Gravity and Phenomenology, Feb. 2004 Polan