  While type Ia Supernovae (SNe Ia) have been used as precise cosmological
distance indicators, their progenitor systems remain unresolved. One of the key
questions is if there is a non-degenerate companion star at the time of a
thermonuclear explosion of a white dwarf (WD). In this paper, we investigate if
an interaction between the SN ejecta and the companion star may result in
observable footprints around the maximum brightness and thereafter, by
performing multi-dimensional radiation transfer simulations based on
hydrodynamic simulations of the interaction. We find that such systems result
in variations in various observational characteristics due to different viewing
directions, while the predicted behaviors (redder and fainter for the companion
direction) are opposite to what were suggested by the previous study. The
variations are generally modest and within observed scatters. However, the
model predicts trends between some observables different from observationally
derived, thus a large sample of SNe Ia with small calibration errors may be
used to constrain the existence of such a companion star. The variations in
different colors in optical band passes can be mimicked by external
extinctions, thus such an effect could be a source of a scatter in the peak
luminosity and derived distance. After the peak, hydrogen-rich materials
expelled from the companion will manifest themselves in hydrogen lines.
H$\alpha$ is however extremely difficult to identify. Alternatively, we find
that P$_{\beta}$ in post-maximum near-infrared spectra can potentially provide
powerful diagnostics.
