Inflationary models predict a correlation between primordial density
perturbations (scalar metric perturbations) and gravitational waves (tensor
metric perturbations) in the form of a scalar-scalar-tensor three-point
correlation, or bispectrum in Fourier space. The squeezed limit of this
bispectrum implies a quadrupolar asymmetry in the observed local power spectrum
for matter and galaxies. Here we show (like others before) that an infrared
divergence in the amplitude of this power asymmetry predicted in single-field
slow-roll models is canceled by projection effects when considering the
observed power spectrum. We then further evaluate the nonzero, but finite,
residual quadrupolar power asymmetry that remains after the divergences are
canceled. While the quadrupolar power asymmetry is small, it is conceptually
important. Our calculation moreover clarifies how the predictions for this
power asymmetry may change in models with different scalar-scalar-tensor
bispectra, and shows that convincing detection of the quadrupolar power
asymmetry would rule out the single-field slow-roll models of inflation.Comment: 20 pages, 3 figures, revised to match the published versio
