theoretically or empirically (see, e.g., @Mazeh:2006vh), particularly in the mass range of the progenitors of SNe Ia, suggesting that substantial room for improvement exists on both fronts in this regime.

![The cosmic rate of Type Ia supernovae. Shown are recent measurements from LOSS [@Li:2010iii], SDSS [@Dilday:2010qk], SCP [@Kuznetsova:2007ew], HST [@Dahlen:2008uj], SNLS [@Gonzalez] and Subaru Deep Field [@Graur]. A model assuming only a fixed $\Delta t^{-1}$ delay time distribution and the cosmic SFR from @Kistler09 ([*thick solid line*]{}) can be compared to our models incorporating metallicity dependence (see text), which use either a $\Delta t^{-0.9}$ DTD ([*thick dotted line*]{}) or $\Delta t^{-0.8}$ DTD ([*thick dashed line*]{}). The components of these models with delays from stellar birth to explosion of less than 1 Gyr (“prompt”) and greater than 1 Gyr (“delayed”) are also shown ([*thin lines*]{}; as labelled).\
\[Iahist\]](Iahist){width="3.38in"}

The Cosmic Type Ia Supernova Rate {#section:v}
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We next examine the expectations for the cosmic rate of SNe Ia by first considering a case without explicit metallicity dependence. We proceed by returning to Eq. (\[eq:rate\]) with the comoving star formation rate density $\dot{\rho}_*(z)$ inferred up to $z \sim 8$, using the @Yuksel:2008cu parametrization of the star formation history (SFH), $$\begin{aligned}
      \dot{\rho}_*(z)
      & 