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

TL;DR

This work investigates an emergent, non‑singular universe within the Modified Chaplygin Gas framework by leveraging a first‑order approximation to obtain an explicit analytical form for the scale factor, $a(t)$. The model yields a smooth transition from a quasi‑static early state to a de Sitter‑like late expansion, approaching the $\Lambda$CDM limit, and is constrained by Hubble data to small, positive $\\alpha$ and $A$ values, with the present age around $13.8$–$13.9$ Gyr. A complementary formulation delivers an exact $a(t)$ of the form $a(t)=a_0\\sinh^{n}(\\omega t)$, enabling explicit predictions of the flip time $t_f$ and the redshift $z_f$, while a Raychaudhuri‑based analysis corroborates the flip and overall dynamics. The study also explores a phantom ( $c<0$ ) regime that yields an emergent universe with a finite past scale factor, linking to phantom scalar field realizations and maintaining consistency with observational constraints. Overall, the MCG framework furnishes a singularity‑free history that reproduces ΛCDM at late times and remains compatible with current cosmological observations without invoking additional exotic fields.

Abstract

The Modified Chaplygin Gas (MCG) model is revisited to examine its ability to describe the full cosmic evolution within a single framework. Because the field equations are highly nonlinear, no closed analytical solution for the scale factor in terms of cosmic time exists. To address this limitation and determine the flip time along with other physical characteristics, we introduce an alternative first order approximation that yields an exact analytical expression for the scale factor. This approach gives rise to an emergent, non singular cosmological scenario in which the universe begins with a finite minimum size and evolves smoothly from a quasi static phase to a de Sitter like expansion at late times, naturally approaching the LambdaCDM limit. Using Hubble observational data, we constrain the equation of state parameters and obtain the viable ranges 0 < alpha < 1 and 0 < A < 1/3. The effective equation of state parameter evolves from a positive value in the early matter dominated era to approximately minus one at late times, consistent with observations. A complementary analysis based on the Raychaudhuri equation further supports the robustness of the model.

Figures (14)

• Figure 1: The variations of $q$ and $z$.
• Figure 2: The variations of $w_{\text{eff}}$ and $z$.
• Figure 3: The variation of $\rho$ with $z$ is shown in this figure.
• Figure 4: $H(z)$ vs $z$
• Figure 5: $\Omega_m$ vs $\alpha$ graph with liklihood