Figure of merit for dark energy constraints from current observational data

June 2008 • 2008PhRvD..77l3525W

Authors • Wang, Yun

Abstract • In order to make useful comparisons of different dark energy experiments, it is important to choose the appropriate figure of merit (FoM) for dark energy constraints. Here we show that for a set of dark energy parameters {f_i}, it is most intuitive to define FoM=1/det⁡Cov(f₁,f₂,f₃,…), where Cov(f₁,f₂,f₃,…) is the covariance matrix of {f_i}. In order for this FoM to represent the dark energy constraints in an optimal manner, the dark energy parameters {f_i} should have clear physical meaning and be minimally correlated. We demonstrate two useful choices of {f_i} using 182 SNe Ia (from the HST/GOODS program, the first year Supernova Legacy Survey, and nearby SN Ia surveys), [R(z_*),l_a(z_*),Ω_bh²] from the five year Wilkinson Microwave Anisotropy Probe observations, and Sloan Digital Sky Survey measurement of the baryon acoustic oscillation scale, assuming the Hubble Space Telescope prior of H₀=72±8(km/s)Mpc^-1, and without assuming spatial flatness. We find that for a dark energy equation of state linear in the cosmic scale factor a, the correlation of (w₀,w_0.5) [w₀=w_X(z=0), w_0.5=w_X(z=0.5), with w_X(a)=3w_0.5-2w₀+3(w₀-w_0.5)a] is significantly smaller than that of (w₀,w_a) [with w_X(a)=w₀+(1-a)w_a]. In order to obtain model-independent constraints on dark energy, we parametrize the dark energy density function X(z)=ρ_X(z)/ρ_X(0) as a free function with X_0.5, X_1.0, and X_1.5 [values of X(z) at z=0.5, 1.0, and 1.5] as free parameters estimated from data. If one assumes a linear dark energy equation of state, current observational data are consistent with a cosmological constant at 68% C.L. If one assumes X(z) to be a free function parametrized by (X_0.5,X_1.0,X_1.5), current data deviate from a cosmological constant at z=1 at 68% C.L., but are consistent with a cosmological constant at 95% C.L. Future dark energy experiments will allow us to dramatically increase the FoM of constraints on (w₀,w_0.5), and of (X_0.5,X_1.0,X_1.5). This will significantly shrink the dark energy parameter space to either enable the discovery of dark energy evolution, or the conclusive evidence for a cosmological constant.

Links

• PREPRINT http://arxiv.org/abs/0803.4295
• DATA https://archive.stsci.edu/mastbibref.php?bibcode=2008PhRvD..77l3525W
• DATA https://hst.esac.esa.int/ehst/#/pages/search;bibcode=2008PhRvD..77l3525W
• ELECTR http://link.aps.org/doi/10.1103/PhysRevD.77.123525
• SPIRES http://inspirehep.net/search?p=find+eprint+arXiv:0803.4295