Dark energy and negative compressibility of the Universe: A study based on cosmic equations of state
All cosmological models are defined through energy and matter, which describe the evolution of the targeted Universe. Whether the content is simple or complex, it can be defined through an effective equation of state (EoS). We study different cosmological models by analyzing the properties of the complete EoS of their fluid contents. We obtained general expressions for the ratio between pressure $p$ and energy density $ρ$, and for their derivative $dp/dρ$ in terms of deceleration and jerk parameters. We show that, in general, a cosmology whose energy density is constructed from multiple ideal gases cannot be described by the EoS of a single, ideal gas. This is directly related to a variation in the deceleration parameter during the evolution of the Universe. Furthermore, we studied the effective compressibility properties of the EoS, demonstrating that dark energy features of the fluid should be related to the negative compressibility of the contents. These features depend on the dynamics of the jerk parameter for each cosmological system, implying that the knowledge of dark energy evolution is encoded in the third-order derivatives of the scale factor. This approach to understanding the properties of cosmological models indicates that the accelerating evolution of some models, such as the lambda-cold dark matter model ($Λ$CDM) or the Chaplygin gas model, is due to the EoS of their nonideal content fluids rather than an associated anomalous (dark energy) nature. On the contrary, models such as $w$-cold dark matter ($w$CDM), $w_0$$w_a$-cold dark matter ($w_0$$w_a$CDM), or Dvali-Gabadadze-Porrati models, include by construction fluids with anomalous content, implying a negative compressibility and an effective dark energy behavior. Our work highlights the importance of treating all contents of the Universe as a nonideal fluid system, with a unique EoS.