DOI: 10.1140/epjc/s10052-026-15934-3 ISSN: 1434-6052
Quantum Einsteinian cubic cosmology
Nephtalí Eliceo Martínez Pérez, Cupatitzio Ramírez Romero 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
$$\dot{a}(t)$$
a
˙
(
t
)
, 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.