Gamma ray bursts ( GRBs ) have recently attracted much attention as a possible way to extend the Hubble diagram to very high redshift .
However , the large scatter in their intrinsic properties prevents directly using them as distance indicator so that the hunt is open for a relation involving an observable property to standardize GRBs in the same way as the Phillips law makes it possible to use Type Ia Supernovae ( SNeIa ) as standardizable candles .
We use here the data on the X - ray decay curve and spectral index of a sample of GRBs observed with the Swift satellite .
These data are used as input to a Bayesian statistical analysis looking for a correlation between the X - ray luminosity L _ { X } ( T _ { a } ) and the time constant T _ { a } of the afterglow curve .
We find a linear relation between \log { [ L _ { X } ( T _ { a } ) ] } and \log { [ T _ { a } / ( 1 + z ) ] } with an intrinsic scatter \sigma _ { int } = 0.33 comparable to previously reported relations .
Remarkably , both the slope and the intrinsic scatter are almost independent on the matter density \Omega _ { M } and the constant equation of state w of the dark energy component thus suggesting that the circularity problem is alleviated for the L _ { X } - T _ { a } relation .