  Measuring spectral distortions (SDs) of the cosmic microwave background (CMB)
will provide new constraints on previously unexplored scales of the primordial
power spectrum, allowing us to extend the probed parameter space by several
orders of magnitude in $k$-space, which could have significant implications in
the context of primordial black holes and gravitational waves, among others.
Here we discuss how various models of inflation can be tightly constrained by
the combination of current and future CMB SD and anisotropy experiments. In
particular, we investigate the constraining power of SD experiments such as
FIRAS, PIXIE, and PRISM in conjunction with CMB anisotropy probes such as
Planck or CMB-S4 plus LiteBIRD. Building on the latest version of the Boltzmann
solver CLASS (v3.0), here we also consistently marginalize over the possible
galactic and extra-galactic foregrounds for the SD missions. With this
numerical setup, we are able to realistically forecast the improvements that
the increased lever-arm provided by the addition of the various SD missions
will bring for several combinations of the aforementioned experiments. As a
result, in all considered models we observe that SDs provide a highly
significant tightening of the constraints by up to 640%, and increase the
figure of merit up to a factor of around 1600.
