https://doi.org/10.1140/epjc/s10052-026-15934-3
Regular Article - Theoretical Physics
Quantum Einsteinian cubic cosmology
Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, 72570, Puebla, Puebla, Mexico
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Received:
3
April
2026
Accepted:
1
June
2026
Published online:
22
June
2026
Abstract
We study Cosmological Einsteinian Cubic Gravity (CECG) in the context of minisuperspace quantum cosmology. CECG is a modification of Einstein’s gravity by cubic curvature terms that contribute non-trivially to the dynamics of FRW backgrounds, while the Friedmann equations remain second-order. First, we perform the Hamiltonian analysis of the one-dimensional FRW CECG action. Since the variable canonically conjugate to the scale factor, a(t), is a polynomial of degree five in 
, we implement canonical transformations that enable us to write the Hamiltonian explicitly. Second, we perform the Wheeler–DeWitt (WDW) quantization using the new canonical pairs. The Hamiltonian carries a non-local inverse operator that we handle with a convenient ordering choice or by series expansion. Although there are no other degrees of freedom besides a(t), our non-standard Hamiltonian yields a higher-derivative WDW equation, for which we obtain exact analytic and WKB approximate solutions for the spatially flat and closed cases, respectively. Finally, we introduce a scalar field with inflationary potential and describe WKB wave functions leading to strong correlations between coordinates and momenta.
© The Author(s) 2026
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