Dilatonic ghost condensate as dark energy

TL;DR

The paper addresses the challenge of phantom-like dark energy within a string-inspired framework by using a dilaton with a negative kinetic term stabilized through higher-order kinetic terms, ensuring quantum stability. It derives a general scalar-field Lagrangian of the form $p(X,\varphi)=X g(Xe^{\lambda\varphi})$ to support scaling attractors, and analyzes phase-space dynamics for various parameter choices, including couplings to dark matter ($Q$). The authors show that stable attractors exist for $Q=0$ (leading to a de Sitter-like fate) and for scenarios where $Q$ grows to a constant value, yielding viable scaling solutions with $\Omega_φ\approx0.7$ and $w_φ\approx-0.9$; however, constant large $Q$ can destabilize the vacuum unless the coupling evolves. Overall, the work provides a string-motivated, quantum-stable phantom dark-energy model with rich late-time dynamics and potential to address the coincidence problem via scaling solutions.

Abstract

We explore a dark energy model with a ghost scalar field in the context of the runaway dilaton scenario in low-energy effective string theory. We address the problem of vacuum stability by implementing higher-order derivative terms and show that a cosmologically viable model of ``phantomized'' dark energy can be constructed without violating the stability of quantum fluctuations. We also analytically derive the condition under which cosmological scaling solutions exist starting from a general Lagrangian including the phantom type scalar field. We apply this method to the case where the dilaton is coupled to non-relativistic dark matter and find that the system tends to become quantum mechanically unstable when a constant coupling is always present. Nevertheless, it is possible to obtain a viable cosmological solution in which the energy density of the dilaton eventually approaches the present value of dark energy provided that the coupling rapidly grows during the transition to the scalar field dominated era.

Figures (6)

• Figure 1: The region in which the conditions (\ref{['xi']}) and $\Omega_\varphi \le 1$ are satisfied for (A) $c_1=1$, $c_2=0$ and (B) $c_1=1$, $c_2=1$. In the case (A) each curve or line corresponds to (i) $z^2=(3c_1x^4)/(x^2+1)$ and (ii) $z^2=2c_1x^2$, whereas in the case (B) each corresponds to (i) $z^2=\frac{1}{2c_2} \left[x^2+1 \pm \sqrt{(x^2+1)^2-12c_2x^4} \right]$, (ii) $z^2=2c_1x^2$ and (iii) $z^2=\sqrt{c_1/c_2}\,x^2$.
• Figure 2: The variation of $\Omega_m$, $\Omega_\varphi$, $w_\varphi$, $x^2$ and $z^2$ for $c_1=1$, $c_2=0$ and $\lambda=0.1$ with initial conditions $x_i = 0.0085$ and $z_i =0.0085$. The solution evolves toward the attractor characterized by constant $x^2$ and $z^2$ with $\Omega_\varphi \to 1$ and $\Omega_m \to 0$. The equation of state asymptotically approaches a constant value $w_\varphi \simeq -0.889$.
• Figure 3: The variation of $\Omega_m$, $\Omega_\varphi$, $w_\varphi$, $x^2$ and $z^2$ for $c_1=1$, $c_2=1$ and $\lambda=0.1$ with initial conditions $x_i = 0.003$ and $z_i =0.0035$. The evolution of $\Omega_\varphi$ and $\Omega_m$ is similar to Fig. \ref{['evon']}, although the asymptotic values of $x^2$, $z^2$ and $w_\varphi$ are different.
• Figure 4: The phase-space trajectories for $Q=0.678$ and $\lambda=0.398$ for $c_1=1$ and $c_2=0$. In this case there exist scaling solutions that asymptotically approach $\Omega_\varphi \simeq 0.7$ and $w_\varphi \simeq -0.9$, as long as the initial values of $x^2$ and $z^2$ are not far from the attractor point $(x_s^2, z_s^2)=(1.295, 2.522)$ (this point is indicated by a black point in the figure). If the initial values of $x^2$ and $z^2$ are much smaller than 1, the trajectories tend to evolve out of the stable region. In particular it happens that the solutions hit the singularities with $z^2=6x^2$ at which the speed of sound diverges.
• Figure 5: The phase-space trajectories for $Q=1.45$ and $\lambda=0.85$ for $c_1=1$ and $c_2=1$. In this case scaling solutions correspond to $x_s^2=0.283$ and $z_s^2=0.505$ with asymptotic values $\Omega_\varphi \simeq 0.7$ and $w_\varphi \simeq -0.9$. As is similar to Fig. \ref{['pspace']} the trajectories tend to be away from the stable region when the initial values of $x^2$ and $z^2$ are much smaller than 1.