We apply the Bayesian concept of ‘ evidence ’ to reveal systematically the nature of dark energy from present and future supernova luminosity distance measurements .
We express the unknown dark energy equation of state w ( z ) as a low order polynomial in redshift and use evidence to find the polynomial order , thereby establishing the minimum order required by the data .
We apply this method to the current supernova data , and with a prior -1 \leq w ( z ) \leq 1 and \Omega _ { m } = 0.3 \pm 0.05 , obtain a large probability of 91 \% for the cosmological constant model , with the remaining 9 \% assigned to the two more complex models tested .
We also investigate the use of evidence for future supernova data sets such as distances obtainable from surveys like the Supernova Acceleration Probe ( SNAP ) .
Given a low uncertainty on the present day matter density we find that , if the underlying dark energy model is only modestly evolving , then a constant w ( z ) fit is sufficient .
However , if the evolution of the dark energy equation of state to linear order is larger than |w _ { 1 } | \stackrel { \scriptstyle \sim } { \scriptstyle > } 0.5 , then the evolution can be established with statistical significance .
For models where we can assume the prior -1 \leq w ( z ) \leq 1 , the correct polynomial order can be established even for modestly evolving equations of state .