Analysis of Vector-Inflation Models Using Dynamical Systems

We analyze two possible vector-field models using the techniques of dynamical systems. The first model involves a U(1)-vector field and the second a triad of SU(2)-vector fields. Both models include a gauge-fixing term and a power-law potential. A dynamical system is formulated and it is found that one of the critical points, for each model, corresponds to inflation, the origin of these critical points being the respective gauge-fixing terms. The conditions for the existence of an inflationary era which lasts for at least 60 efolds are studied.

Towards a proof of the equivalence between FRW background expansion and statistical isotropy

We will expose in this paper our advances towards a proof of the equivalence between FRW background expansion, during some period of time that contains primordial inflation, and the statistical isotropy of the primordial curvature perturbation $zeta$ at the end of this period of time. Our motivation rests on the growing interest in the existence of a preferred direction in the Universe hinted by the continuous presence of anomalies in the CMB data.

Scale and shape dependent non-Gaussianity in the presence of inflationary vector fields

We consider cosmological inflationary models in which vector fields play some role in the generation of the primordial curvature perturbation $zeta$. Such models are interesting because the involved vector fields naturally seed statistical anisotropy in the primordial fluctuations which could eventually leave a measurable imprint on the cosmic microwave background fluctuations. In this article, we estimate the scale and shape dependent effects on the non-Gaussianity (NG) parameters due to the scale dependent statistical anisotropy in the distribution of the fluctuations. For concreteness, we use a power spectrum (PS) of the fluctuations of the quadrupolar form: $P_zeta(vec{k})equiv P_zeta(k)[1+g_zeta(k)(hat{n} cdot hat{k})^2 ]$, where $g_{zeta}(k)$ is the only quantity which parametrizes the level of statistical anisotropy and $hat{n}$ is a unitary vector which points towards the preferred direction. Then, we evaluate the contribution of the running of $g_{zeta}(k)$ on the NG parameters by means of the $delta N$ formalism. We focus specifically on the details for the $f_{rm NL}$ NG parameter, associated with the bispectrum $B_zeta$, but the structure of higher order NG parameters is straightforward to generalize. Although the level of statistical anisotropy in the PS is severely constrained by recent observations, the importance of statistical anisotropy signals in higher order correlators remains to be determined, this being the main task that we address here. The precise measurement of the shape and scale dependence (or running) of statistical parameters such as the NG parameters and the statistical anisotropy level could provide relevant elements for model building and for the determination of the presence (or nonpresence) of inflationary vector fields and their role in the inflationary mechanism.

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

We present the different consistency relations that can be seen as variations of the well known Suyama-Yamaguchi (SY) consistency relation tau_{NL} geqslant ((6/5) f_{NL})^2. It has been claimed that the following variation: tau_{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 tau_{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 zeta. 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 tau_{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)

On the Issue of the zeta Series Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part II: the Trispectrum

We calculate the trispectrum T_zeta of the primordial curvature perturbation zeta, generated during a {it slow-roll} inflationary epoch by considering a two-field quadratic model of inflation with {it canonical} kinetic terms. We consider loop contributions as well as tree level terms, and show that it is possible to attain very high, {it including observable}, values for the level of non-gaussianity tau_{NL} if T_zeta is dominated by the one-loop contribution. Special attention is paid to the claim in JCAP {bf 0902}, 017 (2009) [arXiv:0812.0807 [astro-ph]] that, in the model studied in this paper and for the specific inflationary trajectory we choose, the quantum fluctuations of the fields overwhelm the classical evolution. We argue that such a claim actually does not apply to our model, although more research is needed in order to understand the role of quantum diffusion. We also consider the probability that an observer in an ensemble of realizations of the density field sees a non-gaussian distribution. In that respect, we show that the probability associated to the chosen inflationary trajectory is non-negligible. Finally, the levels of non-gaussianity f_{NL} and tau_{NL} in the bispectrum B_zeta and trispectrum T_zeta of zeta, respectively, are also studied for the case in which zeta is not generated during inflation.

Statistical anisotropy of the curvature perturbation from vector field perturbations

The delta N formula for the primordial curvature perturbation zeta is extended to include vector as well as scalar fields. Formulas for the tree-level contributions to the spectrum and bispectrum of zeta are given, exhibiting statistical anisotropy. The one-loop contribution to the spectrum of zeta is also worked out. We then consider the generation of vector field perturbations from the vacuum, including the longitudinal component that will be present if there is no gauge invariance. Finally, the delta N formula is applied to the vector curvaton and vector inflation models with the tensor perturbation also evaluated in the latter case.