New models of chaotic inflation in supergravity

TL;DR

This work develops a broad class of chaotic inflation models within supergravity by leveraging a canonical superconformal (CSS) framework with a W = S f(Φ) structure and shift-symmetric Kähler potentials. Stabilizing the auxiliary field S (via terms like ζ(S S̄)^2) decouples S fluctuations and yields a single-field inflaton with a tunable potential V(φ) = |f(φ/√2)|^2, while allowing nonminimal gravity coupling through χ (or ξ). By comparing logarithmic and polynomial Kähler potentials, the authors show how to realize a wide range of inflationary dynamics, from φ^2 and φ^4-like regimes to Higgs-like plateaus, and demonstrate the stability conditions for S and the imaginary part of Φ. The framework offers substantial flexibility to fit current and future observational data (n_s, r) and to control non-gaussian perturbations via stabilization parameters, unifying and extending prior supergravity constructions of chaotic inflation.

Abstract

We introduce a new class of models of chaotic inflation inspired by the superconformal approach to supergravity. This class of models allows a functional freedom of choice of the inflaton potential V = |f(φ)|^2. The simplest model of this type has a quadratic potential m^2φ^2/2. Another model describes an inflaton field with the standard symmetry breaking potential λ^2 (φ^2-v^2)^2. Depending on the value of v and on initial conditions for inflation, the spectral index n_s may take any value from 0.97 to 0.93, and the tensor-to-scalar ratio r may span the interval form 0.3 to 0.01. A generalized version of this model has a potential λ^2 (φ^α-v^α)^2. At large φand α> 0, this model describes chaotic inflation with the power law potential φ^{2α}. For α< 0, this potential describes chaotic inflation with a potential which becomes flat in the large field limit. We further generalize these models by introducing a nonminimal coupling of the inflaton field to gravity. The mechanism of moduli stabilization used in these models allows to improve and generalize several previously considered models of chaotic inflation in supergravity.

Figures (5)

• Figure 1: Scalar potential for for $s,\,\gamma = 0$ is given by $V(\phi)= {\lambda^2} (\phi^2-v^2)^2/4$. Inflation occurs either when the field $\phi$ rolls down from its large values, as in the simplest models of chaotic inflation, or when it rolls down from $\phi = 0$, as in new inflation.
• Figure 2: WMAP and predictions of our models. Predictions of the model with the potential ${\lambda^2\over 4} (\phi^2-v^2)^2$ (\ref{['inflpot']}) are bounded by the two blues lines corresponding to the number of e-foldings $N = 50$ and $N = 60$Kallosh:2007wm. The blue stars correspond to this model with $v = 0$ and the inflaton nonminimally coupled to gravity with $\xi \gg 1$ for $N = 50$ and $N = 60$Bezrukov:2007epEinhorn:2009bhFerrara:2010ywLee:2010hjFerrara:2010in. The green dashed lines describe predictions of this model for $v = 0$ and for various values of $\xi$Okada:2010jf, for $N = 50$ and $N = 60$. These results suggest that once one considers arbitrary values of $v$ and increases $\xi$, the blue lines will move to the right and down, as indicated by the green dashed lines. As a result, possible values of $n_s$ and $r$ in this model may span a substantial part of the allowed values of $n_s$ and $r$.
• Figure 3: Scalar potential (\ref{['inflpotmodif']}) of the theory (\ref{['W']}), (\ref{['K']}) with the nonminimal coupling of the inflaton field ${\xi\over 2} \phi^2 R$. This coupling can be introduced by adding $\xi(\Phi^2+ \bar{\Phi}^2)$ to $\Omega^2$ and to the Kähler potential. We present a family of potentials for different values of $\xi$, starting from $\xi = 0$ (upper blue line).
• Figure 4: Scalar potential (\ref{['inflpot3a']}) of the theory (\ref{['W3']}), (\ref{['K3a']}) with the nonminimal coupling of the inflaton field ${\xi\over 2} \phi^2 R$. We present a family of potentials for different values of $\xi$, starting from $\xi = 0$ (upper blue line).
• Figure 5: Predictions of the large field inflation in the model with the potential $V\sim (\phi^\alpha-v^\alpha)^2$ for $v < 1$ and different $\alpha$ in the range of $0< \alpha <2$ are shown by two blue lines corresponding to $N = 60$ and $N = 50$.