Eur. Phys. J. Plus (2022) 137: 117
https://doi.org/10.1140/epjp/s13360-021-02316-9

Regular Article

The effects of dark energy on the early Universe with radiation and an ad hoc potential

¹ Departamento de Modelagem Computacional, Instituto Politécnico, Universidade do Estado do Rio de Janeiro, CEP 28625-570, Nova Friburgo, RJ, Brazil
² Departamento de Física, Centro de Ciências Exatas, Universidade Federal do Espírito Santo, CEP 29075-910, Vitória, ES, Brazil
³ Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, CEP 36036-330, Juiz de Fora, Minas Gerais, Brazil
⁴ Departamento de Matemática, Física e Computação, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, CEP 27523-000, Resende, RJ, Brazil

^a monerat@uerj.br

Received: 27 October 2021
Accepted: 23 December 2021
Published online: 13 January 2022

Abstract

This work analyzes the effects of quantization on a Friedmann–Lemaître–Robertson–Walker model with positive curvature and material content composed of a radiation fluid and a cosmological constant playing the role of the dark energy of the Universe. The quantization of the model was performed to particular potential using the finite difference method in the Crank–Nicolson scheme: solutions of the Wheeler–DeWitt equation are obtained, in the form of finite norm wave packets. The introduction of cosmological constant and a term of ad hoc potential allow to obtain bounce solutions (for certain choices of parameters and initial conditions) with exits for inflation (de Sitter solutions). This occurs after the Universe emerges from its quantum phase by a tunneling mechanism.