  We study the possibility of using the $LiteBIRD$ satellite $B$-mode survey to
constrain models of inflation producing specific features in CMB angular power
spectra. We explore a particular model example, i.e. spectator axion-SU(2)
gauge field inflation. This model can source parity-violating gravitational
waves from the amplification of gauge field fluctuations driven by a
pseudoscalar "axionlike" field, rolling for a few e-folds during inflation. The
sourced gravitational waves can exceed the vacuum contribution at reionization
bump scales by about an order of magnitude and can be comparable to the vacuum
contribution at recombination bump scales. We argue that a satellite mission
with full sky coverage and access to the reionization bump scales is necessary
to understand the origin of the primordial gravitational wave signal and
distinguish among two production mechanisms: quantum vacuum fluctuations of
spacetime and matter sources during inflation. We present the expected
constraints on model parameters from $LiteBIRD$ satellite simulations, which
complement and expand previous studies in the literature. We find that
$LiteBIRD$ will be able to exclude with high significance standard single-field
slow-roll models, such as the Starobinsky model, if the true model is the
axion-SU(2) model with a feature at CMB scales. We further investigate the
possibility of using the parity-violating signature of the model, such as the
$TB$ and $EB$ angular power spectra, to disentangle it from the standard
single-field slow-roll scenario. We find that most of the discriminating power
of $LiteBIRD$ will reside in $BB$ angular power spectra rather than in $TB$ and
$EB$ correlations.
