The different varieties of the Suyama-Yamaguchi consistency relation and its violation as a signal of statistical inhomogeneity

Abstract

We present the different consistency relations that can be seen as variations of the well known Suyama-Yamaguchi (SY) consistency relation τ_{NL} \geqslant ((6/5) f_{NL})^2. It has been claimed that the following variation: τ_{NL} ({\bf k}_1, {\bf k_3}) \geqslant (6/5)^2 f_{NL} ({\bf k}_1) f_{NL} ({\bf k}_3), which we call "the fourth variety", in the collapsed (for τ_{NL}) and squeezed (for f_{NL}) limits is always satisfied independently of any physics; however, the proof depends sensitively on the assumption of scale-invariance which only applies for cosmological models involving Lorentz-invariant scalar fields (at least at tree level), leaving room for a strong violation of this variety of the consistency relation when non-trivial degrees of freedom, for instance vector fields, are in charge of the generation of ζ. With this in mind as a motivation, we explicitly state under which conditions the SY consistency relation has been claimed to hold in its different varieties (implicitly) presented in the literature; as a result, we show for the first time that the variety τ_{NL} ({\bf k}_1, {\bf k}_1) \geqslant ((6/5) f_{NL} ({\bf k}_1))^2, which we call "the fifth variety", is always satisfied even when there is strong scale-dependence as long as statistical homogeneity holds: thus, an observed violation of this specific variety would prevent the comparison between theory and observation, shaking this way the foundations of cosmology as a science. Later, we concern about the existence of non-trivial degrees of freedom, concretely vector fields for which the levels of non-gaussianity have been calculated for very few models, finding that the fourth variety of the SY consistency relation is indeed strongly violated for some specific wavevector configurations while the fifth variety continues to be well satisfied. (Abridged)

LaTex file, 12 pages, 4 figures. v2: minor cosmetic changes, references added and updated, version to be published in Journal of Cosmology and Astroparticle Physics

References in corpus (11)

• Inflationary Universe with Anisotropic Hair
• Vector Inflation
• Non-Gaussianity in the modulated reheating scenario
• The Nature of Primordial Fluctuations from Anisotropic Inflation
• Scalar-Scalar, Scalar-Tensor, and Tensor-Tensor Correlators from Anisotropic Inflation
• Can a vector field be responsible for the curvature perturbation in the Universe?
• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part I: the Bispectrum
• On Classification of Models of Large Local-Type Non-Gaussianity
• Diagrammatic approach to non-Gaussianity from inflation
• Particle Production of Vector Fields: Scale Invariance is Attractive
• Non-Gaussianity Consistency Relation for Multi-field Inflation

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• Anisotropic Scalar Field Dark Energy with a Disformally Coupled Yang-Mills Field
• Scale and shape dependent non-Gaussianity in the presence of inflationary vector fields