Cosmological Dynamics of Phantom Field

TL;DR

The paper investigates the cosmological dynamics of a phantom field with a negative kinetic term to realize $w_\phi < -1$ and drive late-time acceleration. Focusing on an inverse cosh potential, it shows the de Sitter-like state is a robust late-time attractor, with the field initially subdominant and later overtaking the background to yield observed acceleration. Through a detailed phase-space analysis and a specific potential, the authors demonstrate that viable cosmological evolution can occur, ultimately stabilizing at $w_\phi = -1$ and producing $\Omega_\phi \approx 0.7$, $\Omega_m \approx 0.3$. They fit the model to Type Ia supernova data, obtaining best-fit parameters that yield $w_\phi \,\approx\,-1.74$ and allow $-2.4 < w_\phi < -1$ at 95.4% confidence, while highlighting the necessity of fine-tuning and suggesting further constraints from CMB and large-scale structure.

Abstract

We study the general features of the dynamics of the phantom field in the cosmological context. In the case of inverse coshyperbolic potential, we demonstrate that the phantom field can successfully drive the observed current accelerated expansion of the universe with the equation of state parameter $w_φ < -1$. The de-Sitter universe turns out to be the late time attractor of the model. The main features of the dynamics are independent of the initial conditions and the parameters of the model. The model fits the supernova data very well, allowing for $-2.4 < w_φ < -1$ at 95 % confidence level.

Figures (9)

• Figure 1: Evolution of the phantom field is shown for the model described by eqn. (\ref{['pot']}). Due to the unusual behavior, the phantom field, released with zero kinetic energy away from the origin, moves towards the top of the potential. It sets into the damped oscillations about $\phi=0$ and ultimately settles there permanently.
• Figure 2: Phase portrait (plot of $Y_2 \equiv \dot{\phi}/M_p^2$ versus $Y_1 \equiv \phi/M_p$) of the model described by eqn. (\ref{['pot']}). Trajectories starting anywhere in the phase space end up at the stable critical point (0,0).
• Figure 3: The ratio of kinetic to potential energy of the phantom field is plotted for the potential given by eqn. (\ref{['pot']}) for $\alpha=2$ (solid line) and $\alpha=3$ (dashed line). The evolution of $|K_e/P_e|$ starts later but peaks higher for larger value of $\alpha$. The height of the peak is independent of $V_0$. The change in the value of $V_0$ merely shifts the position of the peak.
• Figure 4: The energy density is plotted against the scale factor: solid line corresponds to $\rho_{\phi}$ for $\alpha=1.26$ in case of the model (\ref{['pot']}) with $V_0^{1/4}\simeq 3\times 10^{-30} M_p$. The dashed and dotted lines correspond to energy density of radiation and matter. Initially, the energy density of the phantom field is extremely subdominant and remains to be so for most of the period of evolution. At late times, the field energy density catches up with the background, overtakes it and starts growing ($w_{\phi)}<-1)$ and drives the current accelerated expansion of the universe before freezing to a constant value equal to $-1$ (in future).
• Figure 5: Evolution of the equation of state parameter $w_{\phi}$ is shown as a function of the scale factor for the model described in figure \ref{['figden']} in case of $\alpha=2.5$ (solid line) and $\alpha=2$ (dashed line) . Except for a short period, $w_{\phi}$ is seen to be constant (-1). The parameter evolves to negative values less than -1 (smaller for larger value of $\alpha$) at late times leading to current acceleration of the universe . It then executes damped oscillations and fast stabilizes to $w_{\phi}=-1$.