  Noncommutative geometry can provide effective description of physics at very
short distances taking into account generic effects of quantum gravity.
Inflation amplifies tiny quantum fluctuations in the early universe to
macroscopic scales and may thus imprint high energy physics signatures in the
cosmological perturbations that could be detected in the CMB. It is shown here
that this can give rise to parity-violating modulations of the primordial
spectrum and odd non-Gaussian signatures. The breaking of rotational invariance
of the CMB provides constraints on the scale of noncommutativity that are
competitive with the existing noncosmological bounds, and could explain the
curious hemispherical asymmetry that has been claimed to be observed in the
sky. This introduces also non-Gaussianity with peculiar shape- and
scale-dependence, which in principle allows an independent cross-check of the
presence of noncommutativity at inflation.
