Cosmological determination to the values of the prefactors in the logarithmic corrected entropy-area relation

In this paper, we continue investigating the possible values of the pre-factors $\alpha$ and $\beta$ in the logarithmic corrected entropy-area relation based on cosmological stability arguments. In a previous study, we have investigated the stability of the entropy-corrected cosmology using an empirical hyperbolic form of the scale factor. We found that the zero values of the two pre-factors are necessary to obtain a stable flat universe with a deceleration-acceleration transition and no causality violation. The necessity of the zero values of the two pre-factors has also been reached in the current work using a hybrid scale factor Ansatz in the entropy-corrected cosmological equations. Investigating the corrected entropy-area relation in different gravitational and cosmological contexts can provide an accurate estimation to the correct values of the pre-factors. The current work opens a discussion on the validity of the correction terms in the logarithmic corrected entropy-area relation on the cosmological scale. The evolution of the cosmic pressure, energy density, equation of state parameter, jerk parameter and the nonlinear energy conditions has been analyzed.