CMB signature of a super-Hubble inhomogeneity in the gravitational field
  enclosing the present Hubble volume
  Repeated studies of the CMB based on WMAP data have revealed an apparent
asymmetry in the distribution of temperature fluctuations over the celestial
sphere. The studies indicate that the amplitudes of temperature fluctuations
are higher in one hemisphere than in the other. We consider whether this
asymmetry could originate from a large scale inhomogeneity in the gravitational
field enclosing the present Hubble volume. We examine what effect the presence
of an inhomogeneity in the gravitational field of size larger than the present
Hubble radius would have on the temperature distribution of the CMB and start
eliciting its observational signature in the CMB power spectrum. The covariance
function contains, in addition to the diagonal entries of the conventional CMB
temperature anisostropy power spectrum, non-diagonal entries. We find that
specific non-diagonal entries of the covariance function are sensitive to the
strength of the inhomogeneity, while the diagonal entries are not. These
non-diagonal entries, which are not present in the case of a homogeneous
background geometry, are observational signatures of a large-scale
inhomogeneity in the background geometry of the universe. Furthermore, we find
that an inhomogeneity in the gravitational potential of super-Hubble size would
yield a power asymmetry in the CMB with maximal asymmetry at an angle of 90
degrees to the CMB dipole axis. The axis of the CMB power asymmetry was
recently estimated by Eriksen et. al. to be located at angles between 83 and 96
degrees to the CMB dipole axis, which is consistent with the prediction of our
model. This implies that the location of the observed power asymmetry in the
CMB sky could be accounted for by a large-scale inhomogeneity in the
gravitational field enclosing the present Hubble volume.
