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.