Uncorrelated measurements of the cosmic expansion history and dark energy from supernovae

We present a method for measuring the cosmic expansion history $H(z)$ in uncorrelated redshift bins, and apply it to current and simulated type Ia supernova data assuming spatial flatness. If the matter density parameter ${\Omega }_m$ can be accurately measured from other data, then the dark-energy density history $X(z)={\rho }_X(z)/{\rho }_X(0)$ can trivially be derived from this expansion history $H(z)$. In contrast to customary “black box” parameter fitting, our method is transparent and easy to interpret: the measurement of $H(z{)}^{-1}$ in a redshift bin is simply a linear combination of the measured comoving distances for supernovae in that bin, making it obvious how systematic errors propagate from input to output. We find the Riess et al. (2004) gold sample to be consistent with the vanilla concordance model where the dark energy is a cosmological constant. We compare two mission concepts for the NASA/DOE Joint Dark-Energy Mission (JDEM), the Joint Efficient Dark-energy Investigation (JEDI), and the Supernova Accelaration Probe (SNAP), using simulated data including the effect of weak lensing (based on numerical simulations) and a systematic bias from K corrections. Estimating $H(z)$ in seven uncorrelated redshift bins, we find that both provide dramatic improvements over current data: JEDI can measure $H(z)$ to about 10% accuracy and SNAP to 30%–40% accuracy.

Figure 1

Data used. The measured dimensionless comoving distances are shown for the Riess et al. (2004) gold sample before (top panel) and after (bottom panel) flux averaging. The cosmic expansion $h(z)$ is simply the inverse of the derivative of this, so the visually obvious fact that the derivative is falling immediately tells us that the universe was denser and faster expanding in the past.

Figure 2

The cosmic expansion history [the dimensionless Hubble parameter $h(z)$] is measured in uncorrelated redshift bins from the Riess et al. (2004) gold sample (top panel) and from simulated future data (middle panel) for the NASA/JDEM mission concepts JEDI (solid points) and SNAP (dotted points). The measured $h(z{)}^{-1}$ in a given redshift bin is simply the sum of the comoving supernova distances in that bin, weighted by the corresponding solid curve in the bottom panel, which roughly speaking subtracts more nearby supernovae from more distant ones.

Figure 3

Same as Fig. 2b, but with a systematic bias of $d{m}_{sys}=0.02z$ from K-correction uncertainties added in addition to lensing noise computed from numerical simulations (Barber 2003 [48]).

Figure 4

How the recovery of the cosmic expansion history $h(z)$ depends on the number of redshift bins, assuming no systematic bias and no lensing. (a) Half of JEDI data, with a reduced intrinsic scatter of ${\sigma }_{\mathrm{int}}=0.08$ mag. (b) All of JEDI data, with ${\sigma }_{\mathrm{int}}=0.16\mathrm{mag}$. (c) All of SNAP data (plus 25 SNe Ia at $z<0.1$), with ${\sigma }_{\mathrm{int}}=0.16\mathrm{mag}$.