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We use a sample of about 22,000 galaxies at $0.65<z<1.2$ from the VIPERSPDR-1 catalogue, to constrain the cosmological model through a measurement ofthe galaxy {\it clustering ratio} $\eta_{g,R}$. This statistic has favourableproperties, being defined as the ratio of two quantities characterizing thesmoothed density field in spheres of given radius $R$: the value of itscorrelation function on a multiple of this scale, $\xi(nR)$, and its variance$\sigma^2(R)$. For sufficiently large values of $R$, this is a universalnumber, capturing 2-point clustering information independently of the linearbias and linear redshift-space distortions of the specific galaxy tracers. Inthis paper we discuss in detail how to extend the application of $\eta_{g,R}$to quasi-linear scales and how to control and remove observational selectioneffects which are typical of redshift surveys as VIPERS. We verify the accuracyand efficiency of these procedures using mock catalogues that match the surveyselection process. These results evidence the robustness of $\eta_{g,R}$ tonon-linearities and observational effects, which is related to its verydefinition as a ratio of quantities that are similarly affected.  We measure $\Omega_{m,0}=0.270_{-0.025}^{+0.029}$. In addition to the greatprecision achieved on our estimation of $\Omega_m$ using VIPERS PDR-1, thisresult is remarkable because it appears to be in good agreement with a recentestimate $z\simeq 0.3$, obtained applying the same technique to the SDSS-LRGcatalogue. It, therefore, suports the robustness of the present analysis.Moreover, the combination of these two measurements at $z\sim 0.3$ and $z\sim0.9$ provides us with a very precise estimate $\Omega_{m,0}=0.274\pm0.017$which highlights the great consistency between our estimation and othercosmological probes such as BAOs, CMB and Supernovae.

The VIMOS Public Extragalactic Redshift Survey (VIPERS): $\Omega_{\rm m_0}$ from the galaxy clustering ratio measured at $z \sim 1$