We combine recent long Gamma Ray Bursts ( GRBs ) sample including 52 objects out to z = 6.3 compiled from Swift Gamma Ray Bursts by Schaefer ( 2006 ) with Type Ia Supernova ( SNIa ) , Cosmic Microwave Background ( CMB ) and Baryon Oscillation ( BAO ) to constrain cosmologies .
We study the constraints arising from GRBs alone and the complementarity of GRBs to other cosmological probes .
To analyze the cosmological role of GRBs , we adopt the Hubble constant as a free parameter with a prior in the range of H _ { 0 } = 72 \pm 8 \@math@espace { km s } ^ { -1 } { Mpc } ^ { -1 } instead of a fixed H _ { 0 } used in previous studies .
By jointly using SNIa gold/SNLS samples and GRBs , the constraints on \Omega _ { M } - \Omega _ { \Lambda } parameter space are dramatically improved in comparing with those from SNIa data alone .
The complementarity of GRBs is mostly from the sub-sample with z > 1.5 due to the different parameter degeneracies involved in luminosity distances at different redshifts .
Including GRB data in addition to SNIa , BAO and CMB in our analysis , we find that the concordance model with \Omega _ { M } \sim 0.3 and \Omega _ { \Lambda } \sim 0.7 is still well within 1 \sigma confidence range .