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arXiv · 2603.29304

Quantum Einsteinian Cubic Cosmology

Nephtalí Eliceo Martínez Pérez·Cupatitzio Ramírez Romero
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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.

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Nephtalí Eliceo Martínez Pérez, Cupatitzio Ramírez Romero. 2026-03-31. Quantum Einsteinian Cubic Cosmology. https://doi.org/10.1140/epjc%2Fs10052-026-15934-3

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