  One of the most intriguing hints of a departure from the standard
cosmological model is a large-scale dipolar power asymmetry in the cosmic
microwave background (CMB). If not a statistical fluke, its origins must lie in
the modulation of the position-space fluctuations via a physical mechanism,
which requires the observation of new modes to confirm or refute. We introduce
an approach to describe such a modulation in k space and calculate its effects
on the CMB temperature and lensing. We fit the k-space modulation parameters to
Planck 2015 temperature data and show that CMB lensing will not provide us with
enough independent information to confirm or refute such a mechanism. However,
our approach elucidates some poorly understood aspects of the asymmetry, in
particular that it is weakly constrained. Also, it will be particularly useful
in predicting the effectiveness of polarization in testing a physical
modulation.
