A comprehensive dynamical and phenomenological analysis of structure growth in curvature-modulated coupled quintessence scenario

TL;DR

The paper develops a curvature-modulated interacting dark energy–dark matter model within a quintessence framework, introducing a covariant coupling $Q_0=α κ ρ_m \dotφ\big(1-βR/(6H^2)\big)$ derived from an interaction Lagrangian. Using a 3D autonomous dynamical system in $(x,y,u)$, the authors classify critical points and identify stable attractors $E_±$, $F_±$, and $J_±$ whose existence depends on $(α,λ,β)$; curvature modulation via $β$ acts as a screening mechanism, delaying interactions in the early universe and enabling late-time acceleration with controlled growth of structure. They analyze linear perturbations, compute growth observables $u$, $γ$, and $uσ_8$, and compare background and growth histories to Pantheon+, DESI DR1, and other data, finding good agreement and potential signatures in the growth and cosmographic parameters. Two benchmark scenarios illustrate how stronger curvature screening or stronger coupling shape the cosmic history, including the coincidence problem, and show that the model can reproduce key observables while offering distinctive, testable deviations from ΛCDM. Overall, the framework provides a consistent, observationally viable approach to curvedness-modulated DE–DM interactions with rich background–perturbation phenomenology and concrete paths for future constraints and nonlinear investigations.

Abstract

We investigate an interacting dark energy-dark matter model within the quintessence framework, characterized by the coupling term $Q_0 = ακρ_m \dotφ \left[1 - βR/(6H^2) \right]$, and the scalar field evolves under an exponential potential $V(φ) = V_0 e^{-λκφ}$, with parameters $α$, $λ$, and $β$. Recasting the cosmological equations into a first-order autonomous system using dimensionless variables, we perform a phase space analysis to identify conditions for stable, non-phantom accelerating attractors. The Ricci scalar term, controlled by $β$, significantly affects the stability of critical points, with attractors transitioning to repellers for higher values of $β$. We also analyze linear scalar perturbations, focusing on the matter density contrast $δ_m$ and the growth index $γ$. Additionally, we compute the deceleration and jerk parameters, the Hubble rate, and the distance modulus $μ(z)$, showing good agreement with observational data. The model naturally addresses the cosmic coincidence problem through scalar field tracking behavior. For moderate parameter values, matter perturbations continue to grow into the future, capturing both background and perturbative dynamics effectively. This framework thus offers a consistent and observationally viable approach to interacting dark energy.

Figures (9)

• Figure 4: Density plots showing the variation of the grand equation of state parameter $\omega_{\text{tot}}$ in the $\alpha-\lambda$ parameter space. Left and right panels correspond to $\beta = 0.05$ and $\beta = 0.5$, respectively.
• Figure 5: Variation of curvature modulation parameter with e-folding number. Curves correspond to $(\alpha = 1,\ \lambda = -1,\ \beta = 0.5)$ (blue) and $(\alpha = 2,\ \lambda = 1,\ \beta = 0.05)$ (green).
• Figure 6: Phase-space analysis and background evolution for $\beta = 0.5$. Left: 3D phase-space trajectories in $(x, y, u)$ for $\alpha = 1, \lambda = -1$, showing $E_{+}$ as a stable attractor. Right: Evolution of key cosmological parameters: $\omega_{\text{tot}}$, $\Omega_m$, $\Omega_\phi$, and $r_{\text{mc}}$ as functions of $N = \ln a$.
• Figure 7: Phase-space analysis and background evolution for $\beta = 0.05$. Left: 3D phase-space trajectories in $(x, y, u)$ for $\alpha = 2, \lambda = 1$, showing $F_{+}$ as a stable attractor. Right: Evolution of key cosmological parameters: $\omega_{\text{tot}}$, $\Omega_m$, $\Omega_\phi$, and $r_{\text{mc}}$ as functions of $N = \ln a$.
• Figure 8: Evolution of the coincidence parameter $r_{\text{mc}}$ vs. $N = \ln a$ for $(\alpha=1, \lambda=-1, \beta=0.5)$ (solid) and $(\alpha=2, \lambda=1, \beta=0.05)$ (dashed). Color bar indicates the variation of total EoS parameter ($\omega_{\text{tot}}$).