Interacting Quintessence

TL;DR

The paper addresses the coincidence problem in dark-energy models by introducing an interacting quintessence model in a flat FRW universe and deriving a coupling between cold dark matter and the quintessence field from the requirement of a constant energy-density ratio $r=\rho_M/\rho_S$. It shows that this coupling yields a stable attractor where $\rho_M$ and $\rho_S$ scale with the same power $\nu$ of the scale factor, leading to power-law acceleration when $\nu<2$ and yielding explicit expressions for $\Omega_M$, $\Omega_S$ and an exponential scalar potential $V(\phi)=V_0 e^{-\lambda(\phi-\phi_0)}$, with $\lambda$ determined by $r$ and $\gamma_S$. The interaction is encoded in an effective potential $V_{\rm eff}$ and imposes a concrete acceleration condition $\lambda^2 < 24\pi G \frac{(1-\gamma_S)^2}{(1+r)\gamma_S}$. This framework offers a dynamical alternative to a cosmological constant for explaining late-time acceleration and outlines observational tests, along with open questions about how the coupling is switched on in the early Universe.

Abstract

We demonstrate that a suitable coupling between a quintessence scalar field and a pressureless cold dark matter (CDM) fluid leads to a constant ratio of the energy densities of both components which is compatible with an accelerated expansion of the Universe.