  One of the most compelling tasks of modern cosmology is to constrain the
expansion history of the Universe, since this measurement can give insights on
the nature of dark energy and help to estimate cosmological parameters. In this
letter are presented two new measurements of the Hubble parameter H(z) obtained
with the cosmic chronometer method up to $z\sim2$. Taking advantage of
near-infrared spectroscopy of the few very massive and passive galaxies
observed at $z>1.4$ available in literature, the differential evolution of this
population is estimated and calibrated with different stellar population
synthesis models to constrain H(z), including in the final error budget all
possible sources of systematic uncertainties (star formation history, stellar
metallicity, model dependencies). This analysis is able to extend significantly
the redshift range coverage with respect to present-day constraints, crossing
for the first time the limit at $z\sim1.75$. The new H(z) data are used to
estimate the gain in accuracy on cosmological parameters with respect to
previous measurements in two cosmological models, finding a small but
detectable improvement ($\sim$5 %) in particular on $\Omega_{M}$ and $w_{0}$.
Finally, a simulation of a Euclid-like survey has been performed to forecast
the expected improvement with future data. The provided constraints have been
obtained just with the cosmic chronometers approach, without any additional
data, and the results show the high potentiality of this method to constrain
the expansion history of the Universe at these redshifts.
