Anisotropic Trispectrum of Curvature Perturbations Induced by Primordial Non-Abelian Vector Fields

Abstract

Motivated by the interest in models of the early universe where statistical isotropy is broken and can be revealed in cosmological observations, we consider an SU(2) theory of gauge interactions in a single scalar field inflationary scenario. We calculate the trispectrum of curvature perturbations, as a natural follow up to a previous paper of ours, where we studied the bispectrum in the same kind of models. The choice of a non-Abelian set-up turns out to be very convenient: on one hand, gauge boson self-interactions can be very interesting being responsible for extra non-trivial terms (naturally absent in the Abelian case) appearing in the cosmological correlation functions; on the other hand, its results can be easily reduced to the U(1) case. As expected from the presence of the vector bosons, preferred spatial directions arise and the trispectrum reveals anisotropic signatures. We evaluate its amplitude tau_{NL}, which receives contributions both from scalar and vector fields, and verify that, in a large subset of its parameter space, the latter contributions can be larger than the former. We carry out a shape analysis of the trispectrum; in particular we discuss, with some examples, how the anisotropy parameters appearing in the analytic expression of the trispectrum can modulate its profile and we show that the amplitude of the anisotropic part of the trispectrum can be of the same order of magnitude as the isotropic part.

36 pages, 8 figures

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• Observable non-gaussianity from gauge field production in slow roll inflation, and a challenging connection with magnetogenesis
• Clustering Fossils from the Early Universe
• General CMB and Primordial Trispectrum Estimation
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• Vector Curvaton without Instabilities
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• Gauge-flation trajectories in Chromo-Natural Inflation
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• Observational signatures of anisotropic inflationary models
• Gauge-flation and Cosmic No-Hair Conjecture
• Anisotropic Inflation with Non-Abelian Gauge Kinetic Function
• Non-gaussianity from the trispectrum and vector field perturbations
• Total Angular Momentum Waves for Scalar, Vector, and Tensor Fields
• Parity Violating Statistical Anisotropy
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• On the health of a vector field with (R A^2)/6 coupling to gravity
• Stability analysis of inflation with an SU(2) gauge field
• Limits on statistical anisotropy from BOSS DR12 galaxies using bipolar spherical harmonics
• Seeking Inflation Fossils in the Cosmic Microwave Background
• The Matter Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
• An Estimator for statistical anisotropy from the CMB bispectrum
• The charged inflaton and its gauge fields: preheating and initial conditions for reheating
• Statistical Anisotropy from Vector Curvaton in D-brane Inflation
• Inflationary Dynamics with a Non-Abelian Gauge Field
• Curvature Perturbations from a Massive Vector Curvaton
• The different varieties of the Suyama-Yamaguchi consistency relation and its violation as a signal of statistical inhomogeneity
• The Primordial Curvature Perturbation from Vector Fields of General non-Abelian Groups
• Symmetries of Vector Perturbations during the de Sitter Epoch
• Feynman-like Rules for Calculating n-Point Correlators of the Primordial Curvature Perturbation
• Measuring primordial anisotropic correlators with CMB spectral distortions
• The probability distribution for non-Gaussianity estimators constructed from the CMB trispectrum
• Wigner-Eckart theorem in cosmology: Bispectra for total-angular-momentum waves
• Antisymmetric galaxy cross-correlations as a cosmological probe
• On primordial trispectrum from exchanging scalar modes in general multiple field inflationary models
• Scale and shape dependent non-Gaussianity in the presence of inflationary vector fields
• Modulation of the waterfall by a gauge field
• CMB Anomalies from Imperfect Dark Energy: Confrontation with the Data