Quantum Einsteinian Cubic Cosmology

TL;DR

This paper explores quantum cosmology within Einsteinian Cubic Gravity, deriving exact and approximate solutions to the Wheeler-DeWitt equation for different spatial geometries, incorporating scalar field inflation.

Contribution

It introduces a Hamiltonian formulation and quantization approach for Einsteinian Cubic Gravity in cosmology, providing explicit solutions and analyzing scalar field effects.

Findings

Exact solutions for flat universe case

WKB solutions for closed universe case

Strong correlations between coordinates and momenta in scalar field models

Abstract

We study Cosmological Einsteinian Cubic Gravity (CECG) arXiv:1810.08166v3 in the context of minisuperspace quantum cosmology. CECG is a modification of Einstein's gravity by cubic curvature terms that yield a nontrivial contribution to the dynamics of FRW backgrounds while keeping the Friedmann equations at second order. First, we study the Hamiltonian formulation of the effective one-dimensional FRW CECG action using Ostrogradski's canonical variables and Dirac's algorithm for constrained systems. Since the momentum $p_a$ conjugate to the scale factor is a polynomial of degree five in $\dot{a}$, we implement canonical transformations $(a,p_a)\to (A,P)$ that enable us to write the Hamiltonian constraint explicitly. Second, we perform the Wheeler-DeWitt quantization using the new canonical variables. Although FRW CECG has no extra degree of freedom besides the scale factor, its non-standard Hamiltonian yields a higher-derivative Wheeler-DeWitt equation. We obtain exact solutions for the spatially flat case, and WKB-type solutions for the spatially closed case. Finally, we consider a homogeneous scalar field $\phi$ with inflationary potential and obtain WKB wave functions leading to strong correlations between coordinates and momenta.