Phantom cosmology with arbitrary potential: New accelerating scaling attractors

In this article, we investigate the existence of accelerating scaling solutions in coupled phantom cosmology without assuming any specific potential for the phantom scalar field. The coupling between phantom dark energy and dark matter is motivated by the warm inflationary paradigm, with the dissipation coefficient assumed to be either constant or variable. The evolution equations are written in the form of autonomous systems, whose stability is studied using methods of qualitative analysis of dynamical systems. For this analysis, the only requirement imposed on the otherwise arbitrary phantom potential is that a particular dynamical variable, defined in terms of the potential and its derivative, must be invertible. For such a generic potential, we show that accelerated scaling solutions do exist, for both constant and variable dissipation coefficients. Although there is a limitation to these scaling solutions – specifically, the current stage of accelerated expansion is not preceded by a long enough matter-dominated era – our results show that the existence of a direct coupling between phantom dark energy and dark matter yields great potential for addressing the cosmic coincidence problem.

💡 Research Summary

The paper investigates whether accelerating scaling solutions can arise in phantom dark‑energy models without fixing the scalar‑field potential. The authors work within General Relativity on a flat Friedmann‑Lemaître‑Robertson‑Walker background, assuming a pressureless dark‑matter (DM) component and a phantom scalar field ϕ as the dark‑energy (DE) sector. The key novelty is that the potential V(ϕ) is left arbitrary; the only restriction imposed is that the dimensionless quantity λ(ϕ) ≡ −V₍ϕ₎/(κV) be an invertible function of ϕ. This allows the introduction of a single auxiliary variable λ and a function f(λ)=λ²