Unbiased Estimate of Dark Energy Density from Type I[CLC]a[/CLC] Supernova Data

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Abstract
Type Ia supernovae (SNe Ia) are currently the best probes of the dark energy in the universe. To constrain the nature of dark energy, we assume a flat universe and that the weak energy condition is satisfied, and we allow the density of dark energy, ρX(z), to be an arbitrary function of redshift. Using simulated data from a space-based SN pencil-beam survey, we find that by optimizing the number of parameters used to parameterize the dimensionless dark energy density, f(z) = ρX(z)/ρX(z = 0), we can obtain an unbiased estimate of both f(z) and the fractional matter density of the universe, Ωm. A plausible SN pencil-beam survey (with a square degree field of view and for an observational duration of 1 yr) can yield about 2000 SNe Ia with 0 ≤ z ≤ 2. Such a survey in space would yield SN peak luminosities with a combined intrinsic and observational dispersion of σ(mint) = 0.16 mag. We find that for such an idealized survey, Ωm can be measured to 10% accuracy, and the dark energy density can be estimated to ~20% to z ~ 1.5, and ~20%-40% to z ~ 2, depending on the time dependence of the true dark energy density. Dark energy densities that vary more slowly can be more accurately measured. For the anticipated Supernova/Acceleration Probe (SNAP) mission, Ωm can be measured to 14% accuracy, and the dark energy density can be estimated to ~20% to z ~ 1.2. Our results suggest that SNAP may gain much sensitivity to the time dependence of the dark energy density and Ωm by devoting more observational time to the central pencil-beam fields to obtain more SNe Ia at z > 1.2. We use both a maximum likelihood analysis and a Monte Carlo analysis (when appropriate) to determine the errors of estimated parameters. We find that the Monte Carlo analysis gives a more accurate estimate of the dark energy density than the maximum likelihood analysis.
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