Addressing the circularity problem in the $E_text{p}-E_text{iso}$ correlation of Gamma-Ray Bursts. (arXiv:1811.08934v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Amati_L/0/1/0/all/0/1">Lorenzo Amati</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+DAgostino_R/0/1/0/all/0/1">Rocco D&#x27;Agostino</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Luongo_O/0/1/0/all/0/1">Orlando Luongo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Muccino_M/0/1/0/all/0/1">Marco Muccino</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tantalo_M/0/1/0/all/0/1">Maria Tantalo</a>

Given their huge luminosity and redshift distribution extending up to
$zsim9$, Gamma-Ray Bursts (GRBs) are potentially a very powerful tool for
studying the geometry and the accelerated expansion of the universe. We here
propose a new model-independent technique to overcome the circularity problem
affecting the use of GRBs as distance indicators through the use of $E_{rm
p}$–$E_{rm iso}$ correlation. We calibrate the $E_{rm p}$–$E_{rm iso}$
correlation and find the GRB distance moduli that can be used to constrain dark
energy models.} We use observational Hubble data to approximate the cosmic
evolution through B’ezier parametric curve obtained through the linear
combination of Bernstein basis polynomials. In so doing, we build up a new data
set consisting of 193 GRB distance moduli. We combine this sample with the
supernova JLA data set to test the standard $Lambda$CDM model and its $w$CDM
extension. We place observational constraints on the cosmological parameters
through Markov Chain Monte Carlo numerical technique. Moreover, we compare the
theoretical scenarios by performing the AIC and BIC statistics. For the
$Lambda$CDM model we find $Omega_m=0.397^{+0.040}_{-0.039}$ at the $2sigma$
level, while for the $w$CDM model we obtain $Omega_m=0.34^{+0.13}_{-0.15}$ and
$w=-0.86^{+0.36}_{-0.38}$ at the $2sigma$ level. Our analysis suggests that
$Lambda$CDM model is statistically favoured over the $w$CDM scenario. The
results of our numerical analysis are consistent with previous findings
involving GRB data. Also, the values of $Omega_m$ and $w$ for the $w$CDM model
are in remarkable agreement with those obtained by the Dark Energy Survey
collaboration. No evidence for extension of the $Lambda$CDM model is found.

Given their huge luminosity and redshift distribution extending up to
$zsim9$, Gamma-Ray Bursts (GRBs) are potentially a very powerful tool for
studying the geometry and the accelerated expansion of the universe. We here
propose a new model-independent technique to overcome the circularity problem
affecting the use of GRBs as distance indicators through the use of $E_{rm
p}$–$E_{rm iso}$ correlation. We calibrate the $E_{rm p}$–$E_{rm iso}$
correlation and find the GRB distance moduli that can be used to constrain dark
energy models.} We use observational Hubble data to approximate the cosmic
evolution through B’ezier parametric curve obtained through the linear
combination of Bernstein basis polynomials. In so doing, we build up a new data
set consisting of 193 GRB distance moduli. We combine this sample with the
supernova JLA data set to test the standard $Lambda$CDM model and its $w$CDM
extension. We place observational constraints on the cosmological parameters
through Markov Chain Monte Carlo numerical technique. Moreover, we compare the
theoretical scenarios by performing the AIC and BIC statistics. For the
$Lambda$CDM model we find $Omega_m=0.397^{+0.040}_{-0.039}$ at the $2sigma$
level, while for the $w$CDM model we obtain $Omega_m=0.34^{+0.13}_{-0.15}$ and
$w=-0.86^{+0.36}_{-0.38}$ at the $2sigma$ level. Our analysis suggests that
$Lambda$CDM model is statistically favoured over the $w$CDM scenario. The
results of our numerical analysis are consistent with previous findings
involving GRB data. Also, the values of $Omega_m$ and $w$ for the $w$CDM model
are in remarkable agreement with those obtained by the Dark Energy Survey
collaboration. No evidence for extension of the $Lambda$CDM model is found.

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