Type Ia Supernovae (SNe Ia) are widely used to measure the expansion of the Universe. Improving distance measurements of SNe Ia is one technique to better constrain the acceleration of expansion and determine its physical nature. This document develops a new SNe Ia spectral energy distribution (SED) model, called the SUpernova Generator And Reconstructor (SUGAR), which improves the spectral description of SNe Ia, and consequently could improve the distance measurements. This model is constructed from SNe Ia spectral properties and spectrophotometric data from The Nearby Supernova Factory collaboration. In a first step, a PCA-like method is used on spectral features measured at maximum light, which allows us to extract the intrinsic properties of SNe Ia. Next, the intrinsic properties are used to extract the average extinction curve. Third, an interpolation using Gaussian Processes facilitates using data taken at different epochs during the lifetime of a SN Ia and then projecting the data on a fixed time grid. Finally, the three steps are combined to build the SED model as a function of time and wavelength. This is the SUGAR model. The main advancement in SUGAR is the addition of two additional parameters to characterize SNe Ia variability. The first is tied to the properties of SNe Ia ejecta velocity, the second is correlated with their calcium lines. The addition of these parameters, as well as the high quality the Nearby Supernova Factory data, makes SUGAR an accurate and efficient model for describing the spectra of normal SNe Ia as they brighten and fade. The performance of this model makes it an excellent SED model for experiments like ZTF, LSST or WFIRST.
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