Non-Gaussianities in extended D-term inflation

TL;DR

This paper investigates how extensions of supersymmetric D-term hybrid inflation with multiple light fields can generate significant primordial non-Gaussianities while preserving a scale-invariant power spectrum. The authors develop a multi-field inflationary setup, using the $ abla N$ formalism to relate field fluctuations to curvature perturbations, and derive explicit expressions for the bispectrum and trispectrum, including intrinsics from self-couplings of the isocurvature fields. They analyze both perturbative and non-perturbative (super-Hubble) regimes, identifying parameter domains where $f_{ m NL}$ and $g_{ m NL}$ can be large and predicting how Planck-era constraints on the bispectrum and trispectrum map onto model parameters. The results highlight that joint measurements of the bispectrum and trispectrum are essential to constrain these models, and they establish a framework that connects SUSY hybrid inflation to curvaton-like scenarios via controlled multi-field dynamics and finite-volume effects.

Abstract

We explore extensions of hybrid inflationary models in the context of supersymmetric D-term inflation. We point out that a large variety of inflationary scenarios can be encountered when the field content is extended. It is not only possible to get curvaton type models but also scenarios in which different fields, with nontrivial statistical properties, contribute to the primordial curvature fluctuations. We explore more particularly the parameter space of these multiple field inflationary models. It is shown that there exists a large domain in which significant primordial non-Gaussianities can be produced while preserving a scale free power spectrum for the metric fluctuations. In particular we explicitly compute the expected bi- and trispectrum for such models and compared the results to the current and expected observational constraints. It is shown that it is necessary to use both the bi- and tri-spectra of CMB anisotropies to efficiently reduce their parameter space.

Figures (5)

• Figure 1: Shape of the one-point distribution function of $\overline{\chi}_{1}$ for $H=1$ and $\nu=1$. The solid line corresponds to the equation (\ref{['PDFchib1exp']}) where the imaginary part of $\overline{\chi}$ has been integrated out. The dashed line corresponds to the case where $\overline{\chi}$ is real.
• Figure 2: Diagrammatic representation of the contributions to the connected four point functions of the $\chi_{1}$ component of the complex field $\chi$. The upper line show the Feynman type diagrams that have to be considered in a quantum field approach (for details see for instance 2005PhRvD..72d3514W). For tree order calculations one can equivalently use a classical approach (provided the initial stochastic fields have the properties derived from the free field quantum solutions). The bottom line shows the resulting diagrams where each vertex point then represents a given order in the initial field. The mode dependence of those terms can then easily be derived in the super-horizon limit: the three diagrams that are represented give respectively $P^{\chi_{1}}(k_{2}) P^{\chi_{1}}(\vert {\bf k}_{1}+{\bf k}_{2}\vert)P^{\chi_{1}}(k_{4})$, $P^{\chi_{1}}(k_{2}) P^{\chi_{2}}(\vert {\bf k}_{1}+{\bf k}_{2}\vert)P^{\chi_{1}}(k_{4})$, $P^{\chi_{1}}(k_{2}) P^{\chi_{1}}(k_{3})P^{\chi_{1}}(k_{4})$.
• Figure 3: Exclusion diagrams for parameters $\nu$ and $\overline{\chi}$ for $\theta=\pi/4$ (left panel) and for $\theta=0.1$ (right panel). The locations of the dotted lines where $\overline{\chi}$ is equal to its expected one $\sigma$ fluctuation. The gray areas and solid or short dashed lines correspond to the exclusion zones, obtained by WMAP (solid line) or expected by Planck (short dashed for bispectrum, gray areas for tri-spectrum). The bispectrum constraint corresponds to a straight line (of slope $-2$); the trispectrum is more complicated due to two competing terms in the trispectrum. The long dashed is the location where the terms cancel. We adopted the results of 2006PhRvD..73h3007K on the upperbounds the Planck mission is expected to provide, $f_{\rm NL}=5$ and $\tau_{\rm NL}=560$.
• Figure 4: Example of shapes of the one-point PDF of the local value of $\chi$ in case it underwent a non-perturbative evolution at super-horizon scales. The plots correspond to parameter values $\nu N_{e}^{1/2}=1.5$; the long dashed line to $\overline{\chi}=0$; the solid line to $\overline{\chi}_{1}=0.5$, $\overline{\chi}_{2}=0$ and the short dashed line to $\overline{\chi}_{1}=0$, $\overline{\chi}_{2}=2$ (values of $\overline{\chi}$ are given in units of $H$). The thin solid line is a Gaussian distribution of similar width. The resulting PDF would be the convolution of one of the first distribution with a Gaussian one with arbitrary relative amplitude.
• Figure 5: Behavior of the reduced correlateors, $Q_{3}$ and $Q_{4}$ of the field $\chi_{1}$, as a function of $N_{e}\equiv \log(k_{t}\eta)$. The function $Q_{3}$ (left panel) is to be multiplied by $\nu^2\overline{\chi}_{1}/H^2$; the function $Q_{4}^{\hbox{star}}$ (thick lines of right panel) is to be multiplied by $-\nu^2/H^2$ and the function $Q_{4}^{\hbox{line}}$ (thin lines) is to be multiplied by $2\nu^4(9\overline{\chi}_{1}^2+\overline{\chi}_{2}^2)/H^4$. The dashed lines correspond to the corresponding asymptotic behahiors.