Quintessence and phantom cosmology with non-minimal derivative coupling

TL;DR

The paper analyzes a scalar field with non-minimal derivative coupling to curvature in a flat FRW universe, treating quintessence and phantom cases via a unifying parameter $\varepsilon$. It derives the action, field equations, and cosmological constraints, then investigates zero and constant potentials. Key findings include transitions between two de Sitter phases determined by the coupling, the emergence of a Big Bang or an ever-expanding origin without matter, cosmological turnarounds and bounces (notably in phantom scenarios), and the avoidance or alteration of Big Rip futures. The results show the coupling alone can drive rich cosmological dynamics and motivate extensions to more general models, including quintom-like constructions and cyclic cosmologies.

Abstract

We investigate cosmological scenarios with a non-minimal derivative coupling between the scalar field and the curvature, examining both the quintessence and the phantom cases in zero and constant potentials. In general, we find that the universe transits from one de Sitter solution to another, determined by the coupling parameter. Furthermore, according to the parameter choices and without the need for matter, we can obtain a Big Bang, an expanding universe with no beginning, a cosmological turnaround, an eternally contracting universe, a Big Crunch, a Big Rip avoidance and a cosmological bounce. This variety of behaviors reveals the capabilities of the present scenario.

Figures (8)

• Figure 1: The evolution of $\alpha(t)$ in the phantom case with zero potential. The dash-dotted and dotted lines denote the de Sitter asymptotics $t/3k$ and $t/\sqrt{3}k$, respectively. The solid lines corresponds to $\alpha(t)$ with (a) $(9k^2)^{-1}<\dot\alpha^2<(3k^2)^{-1}$ (case A1); (b) $\dot\alpha^2>(3k^2)^{-1}$ (case A3). We have considered $k^2=\frac{1}{27}$.
• Figure 2: The evolution for $\alpha(t)$ for $\varepsilon=1$ (quintessence), $\Lambda>0$, $\kappa>0$ (case B1). The dashed, dash-dotted, and dotted lines denote de Sitter asymptotics $\alpha(t)=H_\Lambda t$, $t/\sqrt{9\kappa}$, and $t/\sqrt{3\kappa}$, respectively. A solid line corresponds to $\alpha(t)$ with (a) $H_\Lambda^2<\dot\alpha^2<1/9\kappa$; (b) $1/9\kappa<\dot\alpha^2<H_\Lambda^2<1/3\kappa$; (c) $1/9\kappa<\dot\alpha^2<1/3\kappa<H_\Lambda^2$. In graph (a) we have considered $H_\Lambda^2=1$, in graph (b) $H_\Lambda^2={5}$, and in graph (c) $H_\Lambda^2={10}$; everywhere $\kappa=\frac{1}{27}$.
• Figure 3: The evolution for $\alpha(t)$ for $\varepsilon=1$ (quintessence), $\Lambda>0$, $\kappa<0$ (case B2). The dashed line corresponds to the de Sitter solution $\alpha(t)=H_\Lambda t$ with $H_\Lambda<1/\sqrt{3|\kappa|}$. The solid curve corresponds to a solution with $\dot\alpha^2>H_\Lambda^2$. We have considered $H_\Lambda^2=1$ and $\kappa=-\frac{1}{27}$.
• Figure 4: The evolution for $\alpha(t)$ for $\varepsilon=-1$ (phantom), $\Lambda>0$, $\kappa>0$ (case B3). The dashed line corresponds to the de Sitter solution $\alpha(t)=H_\Lambda t$ with $H_\Lambda<1/\sqrt{3\kappa}$. The solid line corresponds to a solution with $\dot\alpha^2<H_\Lambda^2$. We have considered $H_\Lambda^2=1$ and $\kappa=\frac{1}{27}$.
• Figure 5: The evolution of $\alpha(t)$ for $\varepsilon=-1$ (phantom), $\Lambda>0$, $\kappa<0$ (case B4). The dashed, dash-dotted, and dotted lines denote the de Sitter asymptotics $\alpha(t)=H_\Lambda t$, $t/\sqrt{9|\kappa|}$, and $t/\sqrt{3|\kappa|}$, respectively. The solid lines corresponds to $\alpha(t)$ with (a) $H_\Lambda^2<1/9|\kappa|<\dot\alpha^2<1/3|\kappa|$; (b) $H_\Lambda^2<1/9|\kappa|<1/3|\kappa|<\dot\alpha^2$; (c) $1/3|\kappa|<H_\Lambda^2<\dot\alpha^2$; (d) $\dot\alpha^2<H_\Lambda^2<1/9|\kappa|$; (e) $\dot\alpha^2<1/9|\kappa|<H_\Lambda^2$. In graphs (a), (b) and (d) we have considered $H_\Lambda^2=1$, in graphs (c) and (e) $H_\Lambda^2=15$; everywhere $\kappa=-\frac{1}{27}$.