Evolution in the Volumetric Type Ia Supernova Rate from the Supernova
  Legacy Survey
  We present a measurement of the volumetric Type Ia supernova (SN Ia) rate
(SNR_Ia) as a function of redshift for the first four years of data from the
Canada-France-Hawaii Telescope (CFHT) Supernova Legacy Survey (SNLS). This
analysis includes 286 spectroscopically confirmed and more than 400 additional
photometrically identified SNe Ia within the redshift range 0.1<z<1.1. The
volumetric SNR_Ia evolution is consistent with a rise to z~1.0 that follows a
power-law of the form (1+z)^alpha, with alpha=2.11+/-0.28. This evolutionary
trend in the SNLS rates is slightly shallower than that of the cosmic
star-formation history over the same redshift range. We combine the SNLS rate
measurements with those from other surveys that complement the SNLS redshift
range, and fit various simple SN Ia delay-time distribution (DTD) models to the
combined data. A simple power-law model for the DTD (i.e., proportional to
t^-beta) yields values from beta=0.98+/-0.05 to beta=1.15+/-0.08 depending on
the parameterization of the cosmic star formation history. A two-component
model, where SNR_Ia is dependent on stellar mass (Mstellar) and star formation
rate (SFR) as SNR_Ia(z)=AxMstellar(z) + BxSFR(z), yields the coefficients
A=1.9+/-0.1 SNe/yr/M_solar and B=3.3+/-0.2 SNe/yr/(M_solar/yr). More general
two-component models also fit the data well, but single Gaussian or exponential
DTDs provide significantly poorer matches. Finally, we split the SNLS sample
into two populations by the light curve width (stretch), and show that the
general behavior in the rates of faster-declining SNe Ia (0.8<s<1.0) is
similar, within our measurement errors, to that of the slower objects
(1.0<s<1.3) out to z~0.8.
