We show in this paper that it is possible to attain very high, including observable, values for the level of non-gaussianity f N L associated with the bispectrum B ζ of the primordial curvature perturbation ζ, in a subclass of small-field slow-roll models of inflation with canonical kinetic terms. Such a result is obtained by taking care of loop corrections both in the spectrum P ζ and the bispectrum B ζ . Sizeable values for f N L arise even if ζ is generated during inflation. Five issues are considered when constraining the available parameter space: 1. we must ensure that we are in a perturbative regime so that the ζ series expansion, and its truncation, are valid. 2. we must apply the correct condition for the (possible) loop dominance in B ζ and/or P ζ . 3. we must satisfy the spectrum normalisation condition. 4. we must satisfy the spectral tilt constraint. 5. we must have enough inflation to solve the horizon problem.

A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation ζ was developed a few years ago following the spirit of the Feynman rules in Quantum Field Theory. The methodology is very useful and time-saving, as it is for the case of the Feynman rules in the particle physics context, but, unfortunately, is not very well known by the cosmology community. In the present work, we extend such an approach in order to include not only scalar field perturbations as the generators of ζ, but also vector field perturbations. The purpose is twofold: first, we would like the diagrammatic approach (which we would call the Feynman-like rules) to become widespread among the cosmology community; second, we intend to give an easy tool to formulate any correlator of ζ for those cases that involve vector field perturbations and that, therefore, may generate prolonged stages of anisotropic expansion and/or important levels of statistical anisotropy. Indeed, the usual way of formulating such correlators, using the Wick's theorem, may become very clutter and

We study the spectrum P ζ and bispectrum B ζ of the primordial curvature perturbation ζ when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree-level terms (both (either) in P ζ and (or) in B ζ ) and viceversa. The level of non-gaussianity in the bispectrum, fNL, is calculated and related to the level of statistical anisotropy in the power spectrum, g ζ . For very small amounts of statistical anisotropy in the power spectrum, the level of non-gaussianity may be very high, in some cases exceeding the current observational limit.

Inspired in the Standard Model of Elementary Particles, the Einstein Yang-Mills Higgs action with the Higgs field in the SU(2) representation was proposed in Class. Quantum Grav. 32 (2015) 045002 as the element responsible for the dark energy phenomenon. We revisit this action emphasizing in a very important aspect not sufficiently explored in the original work and that substantially changes its conclusions. This aspect is the role that the Yang-Mills Higgs interaction plays at fixing the gauge for the Higgs field, in order to sustain a homogeneous and isotropic background, and at driving the late accelerated expansion of the Universe by moving the Higgs field away of the minimum of its potential and holding it towards an asymptotic finite value. We analyse the dynamical behaviour of this system and supplement this analysis with a numerical solution whose initial conditions are in agreement with the current observed values for the density parameters. This scenario represents a step towards a successful merging of cosmology and well-tested particle physics phenomenology.PACS numbers: 98.80.Cq; 95.36.+x

We use the \delta N formalism to study the trispectrum T_\zeta of the primordial curvature perturbation \zeta when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, \tau_{NL}, is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f_{NL}, and the level of statistical anisotropy in the power spectrum, g_\zeta. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on \tau_{NL} from WMAP, for generic inflationary models, is done.Comment: LaTeX file, 12 pages, no figures. v2: Minor changes, conclusions unchanged. v3: Version accepted for publication in Physics Letters