Tracing dark energy history with gamma ray bursts
  Observations of gamma-ray bursts up to $z\sim 9$ are best suited to study the
possible evolution of the Universe equation of state at intermediate redshifts.
We apply the Combo-relation to a sample of 174 gamma ray bursts to investigate
possible evidence of evolving dark energy parameter $w(z)$. We first build a
gamma ray burst Hubble's diagram and then we estimate the set ($\Omega_m$,
$\Omega_{\Lambda}$) in the framework of flat and non-flat $\Lambda$CDM
paradigm. We then get bounds over the $w$CDM model, where $w$ is thought to
evolve with redshift, adopting two priors over the Hubble constant in tension
at $4.4$-$\sigma$, i.e. $H_0=(67.4\pm0.5)$ km/s/Mpc and $H_0=(74.03\pm1.42)$
km/s/Mpc. We show our new sample provides tighter constraints on $\Omega_m$
since at $z\leq1.2$ we see that $w(z)$ agrees within 1$\sigma$ with the
standard value $w=-1$. The situation is the opposite at larger $z$, where gamma
ray bursts better fix $w(z)$ that seems to deviate from $w=-1$ at $2$-$\sigma$
and $4$-$\sigma$ level, depending on the redshift bins. In particular, we
investigate the $w(z)$ evolution through a piecewise formulation over seven
redshift intervals. From our fitting procedure we show that at $z\geq 1.2$ the
case $w<-1$ cannot be fully excluded, indicating that dark energy's influence
is not negligible at larger $z$. We confirm the Combo relation as a powerful
tool to investigate cosmological evolution of dark energy. Future space
missions will significantly enrich the gamma ray burst database even at smaller
redshifts, improving de facto the results discussed in this paper.
