Inflation in supergravity from field redefinitions

TL;DR

This paper introduces a method to generate new supergravity inflation models by applying field redefinitions to the Kähler potential, expanding the landscape of viable models beyond traditional holomorphic superpotential constraints.

Contribution

It demonstrates how non-holomorphic field redefinitions can produce an infinite variety of supergravity models with the same geometry but different physical properties, including novel inflationary scenarios.

Findings

Constructed multiple inflationary models consistent with observations.

Predicted tensor-to-scalar ratio r in the range [10^{-6}, 0.06].

Included a gravitational reheating mechanism with T_R ~ 10^7 GeV.

Abstract

Supergravity (SUGRA) theories are specified by a few functions, most notably the real K\"ahler function denoted by $G(T_i, \bar {T}_i) = K + \log |W|^2$, where K is a real K\"ahler potential, and W is a holomorphic superpotential. A field redefinition $T_i \rightarrow f_1(T_i)$ does not change neither the theory, nor the K\"ahler geometry. Similarly, the K\"ahler transformation, $K \rightarrow K + f_2 + \bar f_2, W \rightarrow e^{-f_2} W$ where $f_2$ is holomorphic also leaves G and hence the theory and the geometry invariant. However, if we perform a field redefinition only in $K(T_i,\bar{T}_i) \rightarrow K(f(T_i),f(\bar{T}_i))$, while keeping the same superpotential $W(T_i)$, we get a different theory, as G is not invariant under such a transformation while maintaining the same K\"ahler geometry. This freedom of choosing $f(T_i)$ allows constructing an infinite number of new theories given a fixed K\"ahler geometry and a predetermined superpotential W. Our construction generalizes previous ones that were limited by the holomorphic property of $W$. In particular it allows for novel inflationary SUGRA models and particle phenomenology model building, where the different models correspond to different choices of field redefinitions. We demonstrate this possibility by constructing several prototypes of inflationary models (hilltop, Starobinsky-like, plateau, log-squared and bell-curve) all in flat K\"ahler geometry and an originally renormalizable superpotential $W$. The models are in accord with current observations and predict $r\in[10^{-6},0.06]$ spanning several decades that can be easily obtained. In the bell-curve model, there also exists a built-in gravitational reheating mechanism with $T_R\sim \mathcal{O}( 10^7 GeV)$.