We present a measurement of the volumetric Type Ia supernova ( SN Ia ) rate ( \mathrm { SNR } _ { \mathrm { 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 \leq z \leq 1.1 .
The volumetric \mathrm { SNR } _ { \mathrm { Ia } } evolution is consistent with a rise to z \sim 1.0 that follows a power-law of the form ( 1+ z ) ^ { \alpha } , with \alpha = { 2.11 \pm 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. , \propto t ^ { - \beta } ) yields values from \beta = 0.98 \pm 0.05 to \beta = 1.15 \pm 0.08 depending on the parameterization of the cosmic star formation history .
A two-component model , where \mathrm { SNR } _ { \mathrm { Ia } } is dependent on stellar mass ( M _ { \mathrm { stellar } } ) and star formation rate ( SFR ) as \mathrm { SNR } _ { \mathrm { Ia } } ( z ) = A \times M _ { \mathrm { stellar } } ( z ) + B \times \mathrm { % SFR } ( z ) , yields the coefficients A = ( 1.9 \pm 0.1 ) \times 10 ^ { -14 } \mathrm { SNe yr } ^ { -1 } M _ { \odot } ^ { -1 } and B = ( 3.3 \pm 0.2 ) \times 10 ^ { -4 } \mathrm { SNe yr } ^ { -1 } ( M _ { \odot } \mathrm { yr } ^ { % -1 } ) ^ { -1 } .
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 \leq s < 1.0 ) is similar , within our measurement errors , to that of the slower objects ( 1.0 \leq s < 1.3 ) out to z \sim 0.8 .