Measuring dark energy with theE_iso–E_pcorrelation of gamma-ray bursts using model-independent methods

Abstract

We use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the E iso − E p correlation (log E iso = a + b log E p ), where E iso is the isotropic-equivalent gamma-ray energy and E p is the spectral peak energy. We update 42 long GRBs and attempt to constrain the cosmological parameters. The full sample contains 151 long GRBs with redshifts from 0.0331 to 8.2. The first method is the simultaneous fitting method. We take the extrinsic scatter σ ext into account and assign it to the parameter E iso . The best-fitting values are a = 49.15 ± 0.26, b = 1.42 ± 0.11, σ ext = 0.34 ± 0.03 and Ω m = 0.79 in the flat ΛCDM model. The constraint on Ω m is 0.55 < Ω m < 1 at the 1σ confidence level. If reduced χ 2 method is used, the best-fit results are a = 48.96 ± 0.18, b = 1.52 ± 0.08, and Ω m = 0.50 ± 0.12. The second method uses type Ia supernovae (SNe Ia) to calibrate the E iso − E p correlation. We calibrate 90 high-redshift GRBs in the redshift range from 1.44 to 8.1. The cosmological constraints from these 90 GRBs are Ω m = 0.23 +0.06 −0.04 for flat ΛCDM and Ω m = 0.18 ± 0.11 and Ω Λ = 0.46 ± 0.51 for non-flat ΛCDM. For the combination of GRB and SNe Ia sample, we obtain Ω m = 0.271 ± 0.019 and h = 0.701 ± 0.002 for the flat ΛCDM and the non-flat ΛCDM, and the results are Ω m = 0.225 ± 0.044, Ω Λ = 0.640 ± 0.082, and h = 0.698 ± 0.004. These results from calibrated GRBs are consistent with that of SNe Ia. Meanwhile, the combined data can improve cosmological constraints significantly, compared to SNe Ia alone. Our results show that the E iso − E p correlation is promising to probe the high-redshift Universe.

Determination of cosmological parameters from gamma ray burst characteristics and afterglow correlations

“…The Amati relation has been widely used to this aim (Dai et al 2004;Amati et al 2008;Kodama et al 2008;Wei et al 2013;Wang et al 2016). However, this relation was inferred Fig.…”

“…This choice is justified by the fact that y depends on several hidden parameters, while x does not depend on any factor. This has recently been used by Wang et al (2016) to justify the choice of x = E p and y = E iso instead of the reverse, because E iso depends on the cosmological parameters.…”

“…In this work, since we know neither σ x nor σ y we replace m 2 σ 2 x + σ 2 y by σ int , noting that the latter is called extrinsic scatter by (Amati et al 2008;Wang et al 2016) and "intrinsic scatter" by (Dainotti et al 2013a(Dainotti et al , 2016. It replaces the sum of all Gaussian errors that may affect (x, y) and which might come from other nonobserved variabilities.…”

“…For instance, Petrosian et al (2015) investigated the cosmological evolution of a sample of 200 Swift bursts and utilized the results they obtained to put constraints on the star formation rate. Another recent study (Wang et al 2015(Wang et al , 2016 provides a thorough investigation of how GRBs can be employed to constrain cosmological parameters, dark energy, the star formation rate, the pre-galactic metal enrichment, and the first stars (Totani 1997;Wijers et al 1998;Mao and Mo 1998;Mao 2010;Porciani and Madau 2001;Natarajan et al 2005;Hopkins and Beacom 2006;Jakobsson et al 2006;Dermer 2007;Daigne and Mochkovitch 2007;Coward 2007;Yüksel and Kistler 2007;Kistler et al 2008;Dainotti et al 2015b).…”

Spatial Distribution of Gamma-Ray Burst Sources

“…17 and in another on line catalog [18], is used as the basis for the GRB catalog. Our catalog of GRB sources with known red shifts contains a total of 384 objects.…”