Unifying Cosmic Epochs via Quantum-Corrected Expansion with Brane-World Parallels

Abstract

We present an exact, non-perturbative and non-singular ansatz for the universe's expansion history through a novel analytic scale factor, $a(t)=e^{H(t)} { (1-e^{-k(t)t}) }^{b(t)}$, which reproduces the observed sequence of cosmic epochs and bridges inflation to late-time acceleration, as a unified solution, eliminating ad hoc $\Lambda$CDM epoch splicing. The model's dynamically constrained parameters $(H(t), k(t), b(t))$ ensure smooth phase transitions, as confirmed by analytical and numerical analysis of the expansion history. The derived Hubble parameter incorporates quantum-inspired corrections through its functional form, offering a phenomenological approach to integrate quantum effects into classical cosmic evolution. While not derived from fundamental theory, it provides a well motivated framework within brane inspired cosmology with structure exhibiting parallels to brane-world scenarios: the parameter $k(t)$ acts as an effective screening scale, and the non-monotonic $k(t)t$ implies epoch-dependent gravitational coupling. The scaling relation $\sim \rho(t)\lambda(t)$ emerges naturally, offering a unified description of constant and variable-tension brane-like behavior at the phenomenological level.