A microscopic model for inflation from supersymmetry breaking

Abstract

We have proposed recently a framework for inflation driven by supersymmetry breaking with the inflaton being a superpartner of the goldstino, that avoids the main problems of supergravity inflation, allowing for: naturally small slow-roll parameters, small field initial conditions, absence of a (pseudo)scalar companion of the inflaton, and a nearby minimum with tuneable cosmological constant. It contains a chiral multiplet charged under a gauged R-symmetry which is restored at the maximum of the scalar potential with a plateau where inflation takes place. The effective field theory relies on two phenomenological parameters corresponding to corrections to the Kähler potential up to second order around the origin. The first guarantees the maximum at the origin and the second allows the tuning of the vacuum energy between the F- and D-term contributions. Here, we provide a microscopic model leading to the required effective theory. It is a Fayet-Iliopoulos model with two charged chiral multiplets under a second $U\left(1\right)$ R-symmetry coupled to supergravity. In the Brout-Englert-Higgs phase of this $U\left(1\right)$ , the gauge field becomes massive and can be integrated out in the limit of small supersymmetry breaking scale. In this work, we perform this integration and we show that there is a region of parameter space where the effective supergravity realises our proposal of small field inflation from supersymmetry breaking consistently with observations and with a minimum of tuneable energy that can describe the present phase of our Universe.

Fig. 1

a Allowed parameter space (v, x) with $0<v<2.0$ and $0<x<2.0$. The colored regions in which $A_2>0$ can be divided into 4 parts, namely I, II, III and IV. b Region I and part of Region II are in the excluded area where $v^2-\frac{1}{4}x(x-1-v^2)<0$ where the integrating out condition is not satisfied

Fig. 2

The scalar potential for a model in Region I of Fig. 1 with parameters (5.27) is plotted as a function of c and $\rho$ coordinates in a, b respectively. Plot in c shows the relation between $\rho$ and c. The slow-roll parameters $ϵ$ and $\eta$ are shown in d

Fig. 3

The scalar potential for a model in Region II of Fig. 1 with parameters (5.31) is plotted as a function of c and $\rho$ coordinates in a, b, respectively. Plot in c shows the relation between $\rho$ and c

Fig. 4

Plots of the scalar potential in Region III of Fig. 1 with parameters (5.33) as a function of the coordinate c in a and $\rho$ in b. The relation between $\rho$ and c is plotted in c. The slow-roll parameters $ϵ$ and $\eta$ are shown in d

Fig. 5

The scalar potential for a model in Region IV of Fig. 1 with parameters chosen in (5.35) is plotted as a function of c and $\rho$ coordinates in a, b, respectively. Plot in c shows the relation between $\rho$ and c