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

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.