Speaker
Description
The recent DESI DR2 preference for a time-varying dark-energy equation of state, together with the long-standing difficulty of explaining why an initially anisotropic universe should evolve toward isotropy, motivates the study of interacting dark-sector models in anisotropic backgrounds. We investigate the dynamics of Bianchi type-IX cosmologies containing pressureless dark matter coupled to dark energy in the form of a quintessence scalar field $\phi$ with exponential potential $V(\phi)=V_0\,e^{-\lambda\phi}$. Energy exchange between the two dark components is mediated by the scalar field through the interaction term $Q=\kappa\beta\dot\phi\,\rho_{\rm DM}$, where $\kappa^2=8\pi G$ and $\beta$ is a dimensionless coupling. Because Bianchi-IX models generically recollapse, the Hubble scalar $H$ vanishes at the moment of maximum expansion, where the expansion-normalized variables of the standard Wainwright-Ellis formalism diverge. We therefore adopt the $D$-normalized phase-space formalism of Hewitt, Uggla, and Wainwright, which compactifies the state space and remains regular through the recollapse, including the moment of maximum expansion at which $H = 0$. Together with the modified conservation equations for the two dark components, the Einstein Klein Gordon system reduces to a closed autonomous polynomial dynamical system, whose fixed points we classify by linear stability analysis, supplemented by center-manifold theory for the non-hyperbolic points. The fixed points shows the kinetic-dominated, coupling modified matter dominated, curvature scalar, scalar field dominated and coupled scaling families; the last is the anisotropic analogue of the Amendola scaling attractor. Restricting to the initially expanding, isotropizing trajectories, we map the region of the $(\lambda,\beta)$ plane in which anisotropic Bianchi-IX models approach an accelerating Friedmann Robertson Walker state.
