Supersymmetric higher-derivative models in quantum cosmology

TL;DR

This work investigates quantum cosmology for supersymmetric, higher-derivative FLRW models, focusing on Starobinsky-like gravity and its SUSY extensions in 1D supergravity. By recasting higher-derivative actions into classically equivalent, second-order bosonic and first-order fermionic systems, the authors obtain a tractable canonical quantization with linear-in-momentum supercharges, yielding multi-component wavefunctions constrained by SUSY and Hamiltonian relations. They derive both oscillatory (semi-classical) and exact exponential (tunneling) wavefunctions, analyze their inflationary classical limits, and compute initial-curvature probability distributions that resemble no-boundary/tunneling predictions from non-supersymmetric setups. In the N=2 sectors, they obtain exact exponential solutions for arbitrary F(ℛ) and demonstrate how the supersymmetric structure constrains the quantum theory, with implications for boundary conditions and potential SUSY-breaking scenarios. The results open avenues to connect 1D SUSY cosmology with dimensional reductions of 4D supergravity and to explore perturbations and the problem of time in a supersymmetric quantum cosmology context.

Abstract

We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the bosons, and first order for the fermions. Upon quantization, the algebra of fermions leads to a multi-component state, which is annihilated by the Hamiltonian and supersymmetric constraint operators. We obtain asymptotic wave functions of the oscillatory type, whose classical limit corresponds to inflationary evolution, and exact exponential wave functions. We use the latter to derive probability distributions of the initial curvature that are compatible with those obtained using the non-supersymmetric model.

Figures (5)

• Figure 1: WKB solution (\ref{['realsol']}) for $k=1$, $c_1=0$.
• Figure 2: Numerical solution to equations (\ref{['n1eqs']}): (a) $\psi_1(\phi,a)$, (b) $\psi_2(\phi,a)$ for $\alpha=10^3$ and $\kappa=1$.
• Figure 3: Numerical solution to (\ref{['fdrcoupled']}) for $\psi_+$. It grows exponentially in the region of unbounded negative potential.
• Figure 4: Multi-field potential of the N=2 model $V(\varphi,s)\propto (1-e^{-2 c\varphi})^2+e^{-2c \varphi} s^2$.
• Figure 5: Scalar potential $U(a,R,s=0)$. The solid region indicates a negative value.