Embedding (R+R^2)-Inflation into Supergravity

TL;DR

The paper tackles embedding the chaotic inflation scenario of $(R+R^2)$ gravity into $F({\cal R})$ supergravity to overcome the F-term $\eta$-problem. It introduces a cubic $F({\cal R})$ ansatz, $F({\cal R})= -\tfrac{1}{2} f_1 {\cal R} + \tfrac{1}{2} f_2 {\cal R}^2 - \tfrac{1}{6} f_3 {\cal R}^3$, and analyzes the high-curvature regime where inflation occurs, obtaining an effective Lagrangian $L \approx -\tfrac{f_1}{3} R + \tfrac{f_3}{180} (R+R_0)^2$ with $R_0=\tfrac{21 f_1}{f_3}$. By requiring $f_3 \gg 1$ and $f_2^2 \ll f_1 f_3$, the model reproduces Starobinsky-like inflation while preserving a subdominant, nondegenerate scalaron sector, whose mass is $m^2_{\rm scalaron}=\tfrac{f_3 R_0 M_{\rm Pl}^2}{4 f_2^2}$. The authors show that the amplitude of scalar perturbations can be matched with $\Delta_{\cal R}^2 \approx \tfrac{N^2 M^2}{24\pi^2 M_{\rm Pl}^2}$, leading to $f_3 \approx \tfrac{15 M_{\rm Pl}^2}{M^2}$ and $f_3 \sim 6.5\times 10^{10}$ for $N_e \approx 50$, and discuss reheating via scalaron decay and broader SUSY phenomenology. Overall, the work provides a natural, geometrical embedding of chaotic inflation into supergravity with implications for early-universe physics and SUSY breaking.

Abstract

We find the natural embedding of the (R+R^2)-inflationary model into the recently constructed N=1 F(\cal R)-supergravity. It gives a simple and viable realization of chaotic inflation in supergravity. The only requirement for a slow-roll inflation is the existence of the (\cal R)^3-term with an anomalously large coefficient in Taylor expansion of the F(\cal R) function, where \cal R is the covariantly-chiral scalar supercurvature superfield.