A new analysis has refuted cosmological models presented in a previous article published in the European Physical Journal C. The critique focuses on several mathematical inconsistencies detected in the original formulation, which invalidate the conclusions regarding nonlinear interactions and energy exchange in the cosmos. This work underscores the importance of mathematical precision in the construction of theoretical models in cosmology.

This refuting study identifies key errors, including an incorrect simplification of a Liénard-type equation, the unjustified omission of integration constants, and an erroneous use of the variation-of-parameters method. By correcting these deficiencies and deriving the exact analytical solutions, the authors demonstrate that the revised mathematical framework fundamentally contradicts the claims of the original article. This implies that previous conclusions about cosmological dynamics under these interactions are not valid.

The original research proposed scenarios where energy could be exchanged between different components of the universe in a nonlinear fashion, which could have implications for understanding dark matter, dark energy, and the evolution of the universe. However, the current re-evaluation suggests that such interactions, as modeled, cannot be mathematically sustained. This type of critical review is essential for the advancement of theoretical physics, ensuring the robustness of the foundations upon which new hypotheses and models are built.