Dynamical systems analysis of Bianchi type-IX cosmology with a scalar field mediated dark sector interaction
Abstract
The recent DESI DR2 results 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 ϕ with exponential potential V(ϕ)=V0 e−λϕ. Energy exchange between the two dark components is mediated by the scalar field through the interaction term Q=κβϕ̇ ρDM, where κ2=8πG and β 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 equation 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 (λ,β) plane in which anisotropic Bianchi~IX models approach an accelerating Friedmann--Robertson--Walker state.
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BibTeX
@misc{ashmita2026dynamical,
title = {{Dynamical systems analysis of Bianchi type-IX cosmology with a scalar field mediated dark sector interaction}},
author = {Ashmita and Jaturaporn Watanakampolkij and Daris Samart},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35953},
eprint = {2610.35953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35953},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamical systems analysis of Bianchi type-IX cosmology with a scalar field mediated dark sector interaction
AU - Ashmita
AU - Jaturaporn Watanakampolkij
AU - Daris Samart
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.35953
UR - https://arxiv.org/abs/2610.35953
AB - The recent DESI DR2 results 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 ϕ with exponential potential V(ϕ)=V_0 e^−λϕ. Energy exchange between the two dark components is mediated by the scalar field through the interaction term Q=κβϕ̇ ρ_DM, where κ^2=8πG and β 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 equation 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 (λ,β) plane in which anisotropic Bianchi~IX models approach an accelerating Friedmann--Robertson--Walker state.
ER -