We explore the possibility of setting stringent constraints to the Dark Energy equation of state using alternative cosmic tracers like : ( a ) the Hubble relation using HII galaxies , which can be observed at much higher redshifts ( z \raise - 2.0 pt \hbox { \hbox to 0.0 pt { \hbox { $ \sim$ } } \raise 5.0 pt \hbox { $ < $ } } 3.5 ) than those currently traced by SNIa samples , and ( b ) the large-scale structure using the clustering of X-ray selected AGN , which have a redshift distribution peaking at z \sim 1 .

In this paper we use extensive Monte-Carlo simulations to define the optimal strategy for the recovery of the dark-energy equation of state using the high redshift ( z \raise - 2.0 pt \hbox { \hbox to 0.0 pt { \hbox { $ \sim$ } } \raise 5.0 pt \hbox { $ > $ } } 2 ) Hubble relation , but accounting also for the effects of gravitational lensing , which for such high redshifts can significantly affect the derived cosmological constraints .
We investigate the size of the sample of high- z HII-galaxies needed to provide useful constraints in the Dark Energy equation of state .
Based on a “ Figure of Merit ” analysis , we provide estimates for the number of 2 \raise - 2.0 pt \hbox { \hbox to 0.0 pt { \hbox { $ \sim$ } } \raise 5.0 pt \hbox { $ < $ } } z% \raise - 2.0 pt \hbox { \hbox to 0.0 pt { \hbox { $ \sim$ } } \raise 5.0 pt \hbox { $ < $ } } 3.5 tracers needed to reduce the cosmological solution space , presently provided by the Constitution SNIa set , by a desired factor .
The analysis is given for any level of rms distance modulus uncertainty and we find that an expected reduction ( i.e .
by \sim 20 \% - 40 \% ) of the current level of HII-galaxy based distance modulus uncertainty does not provide a significant improvement in the derived cosmological constraints .
It is much more efficient to increase the number of tracers than to reduce their individual uncertainties .

Finally , we propose a framework to put constraints on the dark energy equation of state by using the joint likelihood of the X-ray AGN clustering and of the Hubble relation cosmological analyses .
A preliminary joint analysis using the X-ray AGN clustering of the 2XMM survey and the Hubble relation of the Constitution SNIa set provide : \Omega _ { m } = 0.31 \pm 0.01 and w = -1.06 \pm 0.05 .
We also find that the joint SNIa-2XMM analysis provides significantly more stringent cosmological constraints , increasing the Figure of Merit by a factor \sim 2 , with respect to that of the joint SNIa-BAO analysis .