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 H II galaxies, which can be observed at much higher redshifts (z≲ 3.5) than those currently traced by Type Ia supernovae (SNeIa) samples, and (b) the large-scale structure using the clustering of X-ray selected active galactic nuclei (AGN), which have a redshift distribution peaking at z∼ 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≳ 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 H II 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 ≲z≲ 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 ∼20–40 per cent) of the current level of H II-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 Ωm= 0.31 ± 0.01 and w=−1.06 ± 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 of ∼2, with respect to that of the joint SNIa–baryonic acoustic oscillation analysis.