Building regular cosmologies with an attractor Quasi-de Sitter phase from quantum-modified Friedmann equations

In this paper, we obtain possible cosmologies without big bang singularity. We first get effective modifications of Friedmann equations by using a texture of the first law of thermodynamics with our proposed generalization of the Bekenstein-Hawking entropy. We get modified Friedmann equations leading to a universe without big bang singularity and with maximum allowed values for the Hubble flow, i.e. H-M, and for the energy density, i.e. rho(M). A general study of solutions of the aforementioned equations shows that an emergent universe filled with non-phantom matter arises starting with H-M and with an exponential form for the scale factor a(t) corrected by a decreasing exponential together with regular expressions for rho,H(t),a(t) everywhere. A further feature of these models is that the time derivative of H (H, t) when H = H-M is reached is diverging, also by considering further quantum corrections. Finally, we show that a universe with finite H,t can be easily obtained, for example, with a smooth transition from a phantom universe to a non-phantom one. In this way, we obtain a regular universe with a quasi-de Sitter phase emerging naturally after Planckian times tp without fine tuning.