15788 10.1140/epjc/s10052-026-15788-9 565 126 Einstein–Aether primordial universe with radiation and dark energy 02 Physical Sciences 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics Regular Article - Theoretical Physics Theoretical Physics 1 21 2026 5 4 2026 1 28 2026 4 30 2026 5 22 2026 5 22 The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . 10052 86 86 5 5 A. Oliveira Castro  Junior alessandro.castro@iprj.uerj.br G. A. Monerat monerat@uerj.br G. Oliveira-Neto gilneto@fisica.ufjf.br E. V. Corrêa Silva profeduvasquezuerj@gmail.com.br https://ror.org/0198v2949 grid.412211.5 0000 0004 4687 5267 Departamento de Modelagem Computacional Instituto Politécnico, Universidade do Estado do Rio de Janeiro 28625-570 Nova Friburgo RJ Brazil https://ror.org/04yqw9c44 grid.411198.4 0000 0001 2170 9332 Departamento de Física, Instituto de Ciências Exatas Universidade Federal de Juiz de Fora 36036-330 Juiz de Fora Minas Gerais Brazil https://ror.org/0198v2949 grid.412211.5 0000 0004 4687 5267 Departamento de Matemática, Física e Computação Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro 27537-000 Resende RJ Brazil Abstract We investigate a quantum cosmological model within the framework of Einstein–Aether gravity. The model consists of a positively curved FLRW Universe whose matter content is described by a radiation fluid, in the presence of a positive cosmological constant Λ . We first perform a classical Hamiltonian analysis, constructing the phase space and deriving the dynamics of the scale factor. Notably, we identify specific initial conditions that lead to an inflationary expansion. Subsequently, we quantize the model following Dirac’s formalism, obtaining the Wheeler-DeWitt equation for the wave function of the Universe. We solve this equation numerically and compare our results to those of the WKB approximation, computing quantum tunneling probabilities and the expectation value of the scale factor, along with its standard deviation. Finally, we analyze how these tunneling probabilities are influenced by variations in the fundamental parameters of the theory ( Λ , σ , β ) and the energy of the fluid E. Our results indicate a higher probability for the quantum birth of the Universe in a parameter regime characterized by larger values of Λ , σ , and fluid energy E, together with a smaller value of β .