  Type Ia Supernovae (SNeIa) provided the first evidence of an accelerated
expansion of the universe and remain a valuable probe to cosmology. They are
deemed standardizable candles due to the observed correlations between its
luminosity and photometric features. This characteristic can be exploited to
estimate cosmological distances after accounting for the observed variations.
There is however a remaining dispersion unaccounted for in the current
state-of-the-art standardization methods. In an attempt to explore this issue,
we propose a simple linear 3-component rest-frame flux description for a
light-curve fitter. Since SNIa intrinsic color index variations are expected to
be time-dependent, our description builds-up upon the mathematical expression
of the well known SALT2 for rest-frame flux, whilst we drop the exponential
factor and add an extra model component with time and wavelength dependencies.
The model components are obtained by performing either Principal Component
Analysis (PCA) or Factor Analysis (FA) onto a representative training set. The
constraining power of the Pure Expansion Template for Supernovae (PETS), is
evaluated and we found compatible results with SALT2 for $\Omega_{m0}$ and
$\Omega_{\Lambda 0}$ within 68% uncertainty between the two models, with PETS'
fit parameters exhibiting non negligible linear correlations with SALT2'
parameters. For both model versions we verified that the first component
describes mainly color index variations, as a dominant effect on SNIa spectra.
The model nuisance parameter which multiplies the color index variation-like
fit parameter shows evolution with redshift in an initial binned cosmology
analysis. This behaviour can be due to selection effects. Overall, our model
shows promise, as there are still a few aspects to be refined; however, it
still falls short in reducing the unaccounted dispersion.
