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 in a model-independent manner, we allow the density of dark energy, $\rho_X(z)$, to be an arbitrary function of redshift. Using simulated data from a space-based supernova pencil beam survey, we find that by optimizing the number of parameters used to parametrize 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 $\Omega_m$ (assuming a flat universe and that the weak energy condition is satisfied). A plausible supernova pencil beam survey (with a square degree field of view and for an observational duration of one year) can yield about 2000 SNe Ia with $0\le z \le 2$. Such a survey 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 f(z) can be estimated to $\sim$ 20% to $z \sim 1.5$, and $\sim$ 20-40% to $z \sim 2$, depending on the time dependence of the true dark energy density. Dark energy densities which vary more slowly can be more accurately measured. For the anticipated SNAP mission, $\Omega_m$ can be measured to 14% accuracy, and f(z) can be estimated to $\sim$ 20% to $z \sim 1.2$. Our results suggest that SNAP may gain much sensitivity to the time-dependence of f(z) and $\Omega_m$ by devoting more observational time to the central pencil beam fields to obtain more SNe Ia at z>1.2. We also find that Monte Carlo analysis gives a more accurate estimate of the dark energy density than the maximum likelihood analysis. (abridged)