Forecasts for CMB \mu- and i-type spectral distortion constraints on the
  primordial power spectrum on scales 8 < k < 10^4 Mpc^-1 with the future
  Pixie-like experiments
  Silk damping at redshifts 1.5 x 10^4 < z < 2 x 10^6 erases CMB anisotropies
on scales corresponding to the comoving wavenumbers 8 < k < 10^4 Mpc^-1 (10^5 <
\ell < 10^8). This dissipated energy is gained by the CMB monopole, creating
distortions from a blackbody in the CMB spectrum of the \mu-type and the
i-type. We study, using Fisher matrices, the constraints we can get from
measurements of these spectral distortions on the primordial power spectrum
from future experiments such as Pixie, and how these constraints change as we
change the frequency resolution and the sensitivity of the experiment. We show
that the additional information in the shape of the $i$-type distortions, in
combination with the \mu-type distortions, allows us to break the degeneracy
between the amplitude and the spectral index of the power spectrum on these
scales and leads to much tighter constraints. We quantify the information
contained in both the \mu-type distortions and the i-type distortions taking
into account the partial degeneracy with the y-type distortions and the
temperature of the blackbody part of the CMB. We also calculate the constraints
possible on the primordial power spectrum when the spectral distortion
information is combined with the CMB anisotropies measured by the WMAP, SPT,
ACT and Planck experiments.
