The intrinsic bispectrum of the CMB from isocurvature initial conditions
  Non-linear effects in the early Universe generate non-zero bispectra of the
cosmic microwave background (CMB) temperature and polarization, even in the
absence of primordial non-Gaussianity. In this paper, we compute the
contributions from isocurvature modes to the CMB bispectra using a modified
version of the second-order Boltzmann solver SONG. We investigate the ability
of current and future CMB experiments to constrain these modes with
observations of the bispectrum. Our results show that the enhancement due to
single isocurvature modes mixed with the adiabatic mode is negligible for the
parameter ranges currently allowed by the most recent Planck results. However,
we find that a large compensated isocurvature mode can produce a detectable
bispectrum when its correlation with the adiabatic mode is appreciable. The
non-observation of this contribution in searches for the lensing bispectrum
from Planck allows us to place a new constraint on the relative amplitude of
the correlated part of the compensated isocurvature mode of $f_{\rm
CIP}=1\pm100$. We compute forecasts for future observations by COrE, SO, CMB-S4
and an ideal experiment and conclude that a dedicated search for the bispectrum
from compensated modes could rule out a number of scenarios realised in the
curvaton model. In addition, the CMB-S4 experiment could detect the most
extreme of those scenarios ($f_{\rm CIP}=16.5$) at 2 to 3-$\sigma$
significance.
