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Non-Gaussianity and statistical anisotropy from vector field populated inflationary models

Emanuela Dimastrogiovanni, Nicola Bartolo, Sabino Matarrese, Antonio Riotto

TL;DR

The paper analyzes inflationary scenarios populated by SU(2) vector fields, detailing how non-Abelian self-interactions generate distinctive statistical anisotropy and non-Gaussianity in the curvature perturbation $\zeta$. Using the $\delta N$ formalism and the Schwinger-Keldysh in-in method, it derives analytic expressions for the power spectrum, bispectrum, and trispectrum up to fourth order, separating Abelian (delta-N) and non-Abelian (self-interacting) contributions. It shows that anisotropic signatures, encoded in direction-dependent coefficients, can be as large as or larger than isotropic parts, and that $f_{NL}$ and $\tau_{NL}$ receive correlated vector and non-Abelian contributions with rich parametric dependence. These results provide testable links between non-Gaussianity measurements and statistical anisotropy, offering a path to constrain or detect vector-field-driven inflation with current and future observations.

Abstract

We present a review of vector field models of inflation and, in particular, of the statistical anisotropy and non-Gaussianity predictions of models with SU(2) vector multiplets. Non-Abelian gauge groups introduce a richer amount of predictions compared to the Abelian ones, mostly because of the presence of vector fields self-interactions. Primordial vector fields can violate isotropy leaving their imprint in the comoving curvature fluctuations zeta at late times. We provide the analytic expressions of the correlation functions of zeta up to fourth order and an analysis of their amplitudes and shapes. The statistical anisotropy signatures expected in these models are important and, potentially, the anisotropic contributions to the bispectrum and the trispectrum can overcome the isotropic parts.

Non-Gaussianity and statistical anisotropy from vector field populated inflationary models

TL;DR

The paper analyzes inflationary scenarios populated by SU(2) vector fields, detailing how non-Abelian self-interactions generate distinctive statistical anisotropy and non-Gaussianity in the curvature perturbation . Using the formalism and the Schwinger-Keldysh in-in method, it derives analytic expressions for the power spectrum, bispectrum, and trispectrum up to fourth order, separating Abelian (delta-N) and non-Abelian (self-interacting) contributions. It shows that anisotropic signatures, encoded in direction-dependent coefficients, can be as large as or larger than isotropic parts, and that and receive correlated vector and non-Abelian contributions with rich parametric dependence. These results provide testable links between non-Gaussianity measurements and statistical anisotropy, offering a path to constrain or detect vector-field-driven inflation with current and future observations.

Abstract

We present a review of vector field models of inflation and, in particular, of the statistical anisotropy and non-Gaussianity predictions of models with SU(2) vector multiplets. Non-Abelian gauge groups introduce a richer amount of predictions compared to the Abelian ones, mostly because of the presence of vector fields self-interactions. Primordial vector fields can violate isotropy leaving their imprint in the comoving curvature fluctuations zeta at late times. We provide the analytic expressions of the correlation functions of zeta up to fourth order and an analysis of their amplitudes and shapes. The statistical anisotropy signatures expected in these models are important and, potentially, the anisotropic contributions to the bispectrum and the trispectrum can overcome the isotropic parts.

Paper Structure

This paper contains 13 sections, 53 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Inflation and primordial vector fields
  3. Self-coupled vector field models
  4. Vector-field coupled to gravity
  5. Ackerman-Carroll-Wise (ACW) model
  6. Models with varying gauge coupling
  7. $SU(2)$ vector model: equations of motion for the background and for linear perturbations
  8. Correlation functions of curvature fluctuations: analytic expressions
  9. The power spectrum
  10. Higher-order correlators
  11. Abelian contributions
  12. Non-Abelian contributions
  13. Amplitude of non-Gaussianity: $f_{NL}$ and $\tau_{NL}$

Figures (2)

  • Figure 1: Diagrammatic representations of the tree-level contributions to the vector fields bispectrum.
  • Figure 2: Diagrammatic representations of the tree-level contributions to the vector fields trispectrum: vector-exchange (on the left) and contact-interaction (on the right) diagrams.