A Quadratic Equation of State to Cosmic Acceleration: Entropy Evolution and Phantom Crossing

Abstract

This paper investigates the thermodynamic evolution of the universe within the framework of a quadratic equation of state (EoS). Building upon the basis of the quadratic EoS model, as a phenomenological extension to dark energy models, we analyze the implications for cosmic dynamics, including energy density evolution of effective dark matter and dark energy, entropy behavior, and convexity stability conditions. Our approach emphasizes the significance of thermodynamic principles in understanding the late-time acceleration and the crossing of the phantom divide, providing a cohesive description consistent with recent observational data. Moreover, we demonstrate that the $Λ$CDM model, regardless of entropy additivity, violates the convexity condition, while the quadratic model aligns with maximum entropy and may prevent a \textit{Big Rip} scenario.

Figures (6)

• Figure 3: The evolution of entropy $S(z)$ and its first and second derivatives $S'(z)$ and $S"(z)$ for the effective dark matter dominated model (EMDM) is analyzed with respect to redshift. The plots assume $w_{\rm de} = -1.0003,~ w_{\rm dm} = 0.003, ~ \xi_{\rm de} = 0.0$, and $\xi_{\rm dm} \leq 0.01$. Additionally, the non-negative value of $S"(z)$ for EMDM in the future is shown in the bottom right plot.
• Figure 4: The evolution of entropy $S(z)$ and its first and second derivatives $S'(z)$ and $S"(z)$ for the effective dark energy dominated model (EEDM) is analyzed with respect to redshift. The plots assume $w_{\rm de} = -1.03,~ w_{\rm dm} = 0.0, ~\xi_{\rm de} \leq 0.1$, and $\xi_{\rm dm} = 0.0$. Additionally, the negative value of $S"(z)$ for EEDM in the future is shown in the bottom right plot.
• Figure 5: The evolution of entropy $S(z)$ and its first and second derivatives $S'(z)$ and $S"(z)$ for the model includes of both effective dark matter and dark energy (EMEM) is analyzed with respect to redshift. The plots assume $w_{\rm de} = -1.03,~ w_{\rm dm} = 0.003,~ \xi_{\rm dm} \leq 0.1$, and $\xi_{\rm dm} \leq 0.01$. Additionally, the negative value of $S"(z)$ for EMEM in the future is shown in the bottom right plot.
• Figure 6: The entropy and maximum entropy test of $\Lambda$CDM model.
• Figure 7: The maximum entropy condition for $\Lambda$CDM ($\delta=1.0$) and Tsallis form of it ($\delta\ne 1.0$).