Wang

What Figure of Merit Should We Use to Evaluate Dark Energy Projects?
Yun Wang (Univ. of Oklahoma)

Choosing the appropriate figure of merit (FoM) for dark energy (DE) constraints is key in comparing different DE experiments. I will show that for a set of DE parameters {f_i}, it is most intuitive to define FoM = 1/sqrt[det{Cov(f1,f2,f3,...)}], where Cov(f1,f2,f3,...) is the covariance matrix of {f_i}. The {f_i} should have clear physical meaning, and be minimally correlated. I demonstrate two useful choices of {f_i} using current observational data: (1) (w_0,w_{0.5}), values of w_X(a) at z=0 and z=0.5, with w_X(a) = 3w_{0.5}-2w_0+3(w_0-w_{0.5})a; (2) (X_{0.5}, X_{1.0}, X_{1.5}), values of X(z)=rho_X(z)/rho_X(0) at z=0.5, 1.0, and 1.5, assuming X(z>1.5)=X_{1.5}. Parameter set (1) is significantly less correlated than (w0,wa), and parameter set (2) allows us to obtain minimal model independent constraints on dark energy. Future dark energy experiments should be evaluated using their factors of improvement in FoM of both (w_0,w_{0.5}) and (X_{0.5}, X_{1.0}, X_{1.5}).