The Observed Squeezed Limit of Cosmological Three-Point Functions

Abstract

The squeezed limit of the three-point function of cosmological perturbations is a powerful discriminant of different models of the early Universe. We present a conceptually simple and complete framework to relate any primordial bispectrum in this limit to late time observables, such as the CMB temperature bispectrum and the scale-dependent halo bias. We employ a series of convenient coordinate transformations to capture the leading non-linear effects of cosmological perturbation theory on these observables. This makes crucial use of Fermi Normal Coordinates and their conformal generalization, which we introduce here and discuss in detail. As an example, we apply our formalism to standard slow-roll single-field inflation. We show explicitly that Maldacena's results for the squeezed limits of the scalar bispectrum [proportional to (ns-1) in comoving gauge] and the tensor-scalar-scalar bispectrum lead to no deviations from a Gaussian universe, except for projection effects. In particular, the primordial contributions to the squeezed CMB bispectrum and scale dependent halo bias vanish, and there are no primordial "fossil" correlations between long-wavelength tensor perturbations and small-scale perturbations. The contributions to observed correlations are then only due to projection effects such as gravitational lensing and redshift perturbations.

1 figure, 20 pages. Updated to Journal version

References in corpus (7)

• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Generation and Characterization of Large Non-Gaussianities in Single Field Inflation
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• Primordial gravity wave fossils and their use in testing inflation
• Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
• Resonant Trispectrum and a Dozen More Primordial N-point functions

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