  We investigate whether non-adiabatic perturbations from inflation could
produce an asymmetric distribution of temperature anisotropies on large angular
scales in the cosmic microwave background (CMB). We use a generalised
non-linear $\delta N$ formalism to calculate the non-Gaussianity of the
primordial density and isocurvature perturbations due to the presence of
non-adiabatic, but approximately scale-invariant field fluctuations during
multi-field inflation. This local-type non-Gaussianity leads to a correlation
between very long wavelength inhomogeneities, larger than our observable
horizon, and smaller scale fluctuations in the radiation and matter density.
Matter isocurvature perturbations contribute primarily to low CMB multipoles
and hence can lead to a hemispherical asymmetry on large angular scales, with
negligible asymmetry on smaller scales. In curvaton models, where the matter
isocurvature perturbation is partly correlated with the primordial density
perturbation, we are unable to obtain a significant asymmetry on large angular
scales while respecting current observational constraints on the observed
quadrupole. However in the axion model, where the matter isocurvature and
primordial density perturbations are uncorrelated, we find it may be possible
to obtain a significant asymmetry due to isocurvature modes on large angular
scales. Such an isocurvature origin for the hemispherical asymmetry would
naturally give rise to a distinctive asymmetry in the CMB polarisation on large
scales.
