Measuring the cosmological parameters with theE_p,i-E_isocorrelation of gamma-ray bursts

Abstract

We have used the Ep,i–Eiso correlation of gamma‐ray bursts (GRBs) to measure the cosmological parameter ΩM. By adopting a maximum likelihood approach which allows us to correctly quantify the extrinsic (i.e. non‐Poissonian) scatter of the correlation, we constrain (for a flat universe) ΩM to 0.04–0.40 (68 per cent confidence level), with a best‐fitting value of ΩM∼ 0.15, and exclude ΩM= 1 at >99.9 per cent confidence level. If we release the assumption of a flat universe, we still find evidence for a low value of ΩM (0.04–0.50 at 68 per cent confidence level) and a weak dependence of the dispersion of the Ep,i–Eiso correlation on ΩΛ (with an upper limit of ΩΛ∼ 1.15 at 90 per cent confidence level). Our approach makes no assumptions on the Ep,i–Eiso correlation and it does not use other calibrators to set the ‘zero’ point of the relation, therefore our treatment of the data is not affected by circularity and the results are independent of those derived via Type Ia supernovae (or other cosmological probes). Unlike other multi‐parameters correlations, our analysis grounds on only two parameters, then including a larger number (a factor of ∼3) of GRBs and being less affected by systematics. Simulations based on realistic extrapolations of ongoing (and future) GRB experiments (e.g. Swift, Konus‐Wind, GLAST) show that: (i) the uncertainties on cosmological parameters can be significantly decreased and (ii) future data will allow us to get clues on the ‘dark energy’ evolution.

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.…”

“…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.…”

“…We use the maximum likelihood method as described in (D'Agostini 2005;Amati et al 2008;Dainotti et al 2013aDainotti et al , 2016 to determine correlation relations. The objective is to determine the parameters m and q when interpolating a set of N data points (x i , y i ) by a straight line y = m x + q with standard deviations σ x and σ y .…”

“…We use the maximum likelihood method as described in (D'Agostini 2005; Amati et al 2008;Dainotti et al 2013aDainotti et al , 2016 to constrain the cosmological parameters within the standard ΛCDM model. We should note that in this work we try to constrain the cosmological constants Ω Λ and Ω M while taking a value H 0 = 70 km/s/Mpc for the Hubble constant.…”

“…These two correlations were then used to create a GRB Hubble diagram (Schaefer 2003). Other luminosity and energy correlations were soon discovered, such as: the Amati relation (Amati et al 2002;Amati 2006;Amati et al 2008Amati et al , 2009) which relates the intrinsic spectral peak energy, E p,i , to the equivalent isotropic energy, E iso ; the Yonetoku relation (Yonetoku et al 2004) which is a correlation between E p,i and the isotropic peak luminosity, L iso ; the Ghirlanda relation (Ghirlanda et al , 2006(Ghirlanda et al , 2010 which is a correlation between E p,i and the collimation corrected energy E γ ; and the Liang-Zhang relation (Liang and Zhang 2005) which relates E iso to both E p,i and the break time of the optical afterglow light curves, T a .…”