Beyond the perfect fluid hypothesis for the dark energy equation of state

Abandoning the perfect fluid hypothesis, we investigate here the possibility that the dark energy equation of state (EoS) $w$ is a nonlinear function of the energy density $\rho$. To this aim, we consider four different EoS describing classical fluids near thermodynamical critical points and discuss the main features of cosmological models made out of dust matter and a dark energy term with the given EoS. Each model is tested against the data on the dimensionless coordinate distance to Type Ia Supernovae and radio galaxies, the shift and the acoustic peak parameters and the positions of the first three peaks in the anisotropy spectrum of the comic microwave background radiation. We propose a possible interpretation of each model in the framework of scalar field quintessence determining the shape of the self-interaction potential $V(\varphi )$ that gives rise to each one of the considered thermodynamical EoS. As a general result, we demonstrate that replacing the perfect fluid EoS with more general expressions gives both the possibility of successfully solving the problem of cosmic acceleration escaping the resort to phantom models.

Figure 1

The evolution against the redshift of the dimensionless energy density $\eta (z)$ for the $\mathrm{RK}$ (upper left), $\mathrm{MB}$ (upper right), $\mathrm{Dt}$ (lower left), and $\mathrm{PR}$ (lower right) EoS, respectively. For all models, we set $(q_0,{\Omega }_M)=(-0.5,0.3)$. Short dashed, solid, and long dashed lines refer to different values of $y$, namely $y=0.5$, 0.75, 1.0 for the $\mathrm{RK}$ model, $y=1.5$, 2.5, 3.5 for the $\mathrm{MB}$ one, $y=0.5$, 0.7, 0.9 for the $\mathrm{Dt}$ and $\mathrm{PR}$ models.

Figure 2

The evolution against the redshift of the EoS parameter $w(z)$ for the $\mathrm{RK}$ (upper left), $\mathrm{MB}$ (upper right), $\mathrm{Dt}$ (lower left), and $\mathrm{PR}$ (lower right) EoS, respectively. Model parameters are set as in Fig. 1.

Figure 3

Constraints on the deceleration parameter $q_0$ and the scaled density parameter $y$ for the $\mathrm{MB}$ (left panel), $\mathrm{Dt}$ (central panel), and $\mathrm{PR}$ (right panel) EoS. Models with parameters on the right of the short, solid, and long dashed lines give values of $(l_1,l_2,l_3)$ respectively in agreement within $1\sigma$ with the measured ones. The black dot individuates the best fit model discussed in the text. For all the EoS, ${\Omega }_M$ is set to the best fit value reported in Table .

Figure 4

Reconstructed scalar field potential over the redshift range $(0,10)$ for the models with the $\mathrm{MB}$ (short dashed line), $\mathrm{Dt}$ (solid line), and $\mathrm{PR}$ (long dashed line) EoS. The potential is normalized to be 1 at $z=0$, while, on the abscissa, $\varphi$ is in units of the Planck mass $M_{\mathrm{Pl}}$.