Context : Data from cosmic microwave background radiation ( CMB ) , baryon acoustic oscillations ( BAO ) , and supernovae Ia ( SNe-Ia ) support a constant dark energy equation of state with w _ { 0 } \sim - 1 .
Measuring the evolution of w along the redshift is one of the most demanding challenges for observational cosmology .

Aims : We discuss the existence of a close relation for GRBs , named Combo-relation , based on characteristic parameters of GRB phenomenology such as the prompt intrinsic peak energy E _ { p,i } , the X-ray afterglow , the initial luminosity of the shallow phase L _ { 0 } , the rest-frame duration \tau of the shallow phase , and the index of the late power-law decay \alpha _ { X } .
We use it to measure \Omega _ { m } and the evolution of the dark energy equation of state .
We also propose a new calibration method for the same relation , which reduces the dependence on SNe Ia systematics .

Methods : We have selected a sample of GRBs with 1 ) a measured redshift z ; 2 ) a determined intrinsic prompt peak energy E _ { p,i } , and 3 ) a good coverage of the observed ( 0.3Ð10 ) keV afterglow light curves .
The fitting technique of the rest-frame ( 0.3Ð10 ) keV luminosity light curves represents the core of the Combo-relation .
We separate the early steep decay , considered a part of the prompt emission , from the X-ray afterglow additional component .
Data with the largest positive residual , identified as flares , are automatically eliminated until the p-value of the fit becomes greater than 0.3 .

Results : We strongly minimize the dependency of the Combo-GRB calibration on SNe Ia .
We also measure a small extra-Poissonian scatter of the Combo-relation , which allows us to infer from GRBs alone \Omega _ { M } = 0.29 ^ { +0.23 } _ { -0.15 } ( 1 \sigma ) for the \Lambda CDM cosmological model , and \Omega _ { M } = 0.40 ^ { +0.22 } _ { -0.16 } , w _ { 0 } = -1.43 ^ { +0.78 } _ { -0.66 } for the flat-Universe variable equation of state case .

Conclusions : In view of the increasing size of the GRB database , thanks to future missions , the Combo-relation is a promising tool for measuring \Omega _ { m } with an accuracy comparable to that exhibited by SNe Ia , and to investigate the dark energy contribution and evolution up to z \sim 10 .