Unbiased estimate of dark energy density from type Ia supernova data

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, rho (x)(z), to be an arbitrary function of redshift. Using simulated data from a spacer based SN pencil-beam survey, we find that by optimizing the number of parameters used to parameterize the dimensionless dark energy density, f(z) = rho (x)(z)/rho (x)(z = 0), we can obtain an unbiased estimate of both f(z) and the fractional matter density of the universe, Omega (m). 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. Such a survey 0 less than or equal to z less than or equal to 2 in space would yield SN peak luminosities with a combined intrinsic and observational dispersion of sigma (m(int)) = 0.16 mag. We find that for such an idealized survey, Omega (m) can be measured to 10% accuracy, and the dark energy density can be estimated to similar to 20% to z similar to 1.5, and similar to 20%-40% to z similar to 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, Omega (m) can be measured to 14% accuracy, and the dark energy density can be estimated to similar to 20% to z similar to 1.2. Our results suggest that SNAP may gain much sensitivity to the time dependence of the dark energy density and 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.