Emergent Universe Scenario in the Modified Chaplygin gas : Towards an Exact Solution and Observational Constraints

Abstract

The Modified Chaplygin Gas (MCG) model is revisited as a unified framework for describing cosmic evolution. Due to the nonlinear field equations, exact solutions in cosmic time are generally unavailable; hence, a first-order approximation is employed to obtain the scale factor and flip time. The effective equation-of-state parameter evolves from a positive value in the early universe to $w_{\mathrm{eff}}\approx -1$ at late times, yielding a transition from deceleration to acceleration and approaching the $\Lambda$CDM limit. In the phantom regime, the model admits an emergent solution with a finite minimum scale factor and a late-time de~Sitter--like phase. The emergent solution is geodesically complete and free from curvature singularities, as confirmed by the regular Kretschmann scalar. CMB constraints for all considered cases remain consistent with observations within the $1\sigma$ confidence level, while the combined Hubble-$57$ and CMB analysis provides improved parameter constraints. The solutions are further verified independently using the Raychaudhuri equation, providing an additional consistency check. Overall, the results establish the MCG model as a self-consistent and observationally viable framework for cosmic evolution within general relativity.

36 pages, 36 figures

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