CMB Anisotropies from a Gradient Mode
  A linear gradient mode must have no observable dynamical effect on short
distance physics. We confirm this by showing that if there was such a gradient
mode extending across the whole observable Universe, it would not cause any
hemispherical asymmetry in the power of CMB anisotropies, as long as
Maldacena's consistency condition is satisfied. To study the effect of the long
wavelength mode on short wavelength modes, we generalize the existing second
order Sachs-Wolfe formula in the squeezed limit to include a gradient in the
long mode and to account for the change in the location of the last scattering
surface induced by this mode. Next, we consider effects that are of second
order in the long mode. A gradient mode $\Phi = \boldsymbol q\cdot \boldsymbol
x$ generated in Single-field inflation is shown to induce an observable
quadrupole moment. For instance, in a matter-dominated model it is equal to
$Q=5 (\boldsymbol q\cdot \boldsymbol x)^2 /18$. This quadrupole can be canceled
by superposition of a quadratic perturbation. The result is shown to be a
nonlinear extension of Weinberg's adiabatic modes: a long-wavelength physical
mode which looks locally like a coordinate transformation.
