Anisotropic imprint of long-wavelength tensor perturbations on cosmic structure

TL;DR

This paper investigates the impact of long-wavelength tensor perturbations on cosmic structure, showing that residual quadrupolar asymmetries in the power spectrum are small but significant for testing inflation models.

Contribution

It clarifies how projection effects cancel infrared divergences in the predicted power asymmetry and evaluates the residual quadrupolar asymmetry in various inflation models.

Findings

Infrared divergence in power asymmetry is canceled by projection effects.

Residual quadrupolar asymmetry remains finite and small.

Detection of this asymmetry could rule out single-field slow-roll inflation.

Abstract

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.