Quintessence without scalar fields

TL;DR

This review demonstrates that cosmic acceleration can be modeled without fundamental scalar fields by leveraging (i) a Van der Waals-type equation of state for cosmic fluids, (ii) higher-order curvature terms in $f(R)$ gravity, and (iii) torsion in spacetime geometry. Each route yields effective quintessence-like behavior with negative pressure and is confronted with SN Ia, CMB, and cluster-based observations, attaining fits for $H_0$ near 65–71 km s$^{-1}$ Mpc$^{-1}$ and $\Omega_M\sim0.3$, while predicting plausible ages of the universe. The work highlights that acceleration can emerge from physically motivated modifications to matter or gravity, not solely from scalar-field dynamics, and discusses the observational degeneracies and future probes needed to discriminate among these scenarios. Overall, the paper broadens the landscape of quintessence by grounding it in established physics beyond standard matter content.

Abstract

The issues of quintessence and cosmic acceleration can be discussed in the framework of theories which do not include necessarily scalar fields. It is possible to define pressure and energy density for new components considering effective theories derived from fundamental physics like the extended theories of gravity or simply generalizing the state equation of matter. Exact accelerated expanding solutions can be achieved in several schemes: either in models containing higher order curvature and torsion terms or in models where the state equation of matter is corrected by a second order Van der Waals terms. In this review, we present such new approaches and compare them with observations.

Figures (6)

• Figure 1: The scaled density $x = \rho/\rho_c$ as function of the redshift $z$ for the model with $\gamma = -2.0$. Note that $x$ is confined between $(x_1, x_2)$ (with $x_1(\gamma = -2.0) \simeq 1.823$ and $x_2(\gamma = -2.0) \simeq 0.731$) as discussed in the text.
• Figure 2: The scaled density $x = \rho/\rho_c$ as function of the redshift $z$ for the model with $\gamma = 0.15$. Note that the apparent divergence on the left side is not a physical one, but only an artifact of the scale used in the plot.
• Figure 3: 1, 2 and 3 - $\sigma$ confidence regions in the $(H_0, \gamma)$ plane for the models with $\gamma \in \ ] -3.34186, \ -1 \ ]$.
• Figure 4: 1, 2 and 3 - $\sigma$ confidence regions in the $(H_0, \gamma)$ plane for the models with $\gamma \in \ ] 0.141859, \ 0.151237 \ ]$ having the scaled energy density increasing with the 5red-shift
• Figure 5: The plot shows the behaviour of $\alpha$ and against $n$. It is evident a region in which the power law of the scale factor is more than one and correspondently the parameter $\gamma_{(curv)}$ of state equation is negative .