Viscous Dark Energy and Mass-Varying Dark Matter in Lyra Manifold: Cosmological Dynamics and Observational Constraints

TL;DR

This paper tackles the problem of explaining late-time cosmic acceleration and the coincidence problem within a Lyra-geometry framework that includes a bulk-viscous quintessence field and mass-varying dark matter with DM–DE interaction. It develops an autonomous dynamical system using $x$, $y$, $\Omega_{Lyra}$, and $\Omega_{Viscous}$ with an exponential potential $V(\phi)$ and mass variation $M_m(\phi)$, and analyzes fixed points and their stability to map possible cosmic histories. The study identifies several equilibrium branches, notably a viscous-dominated $P_V$ de Sitter attractor, a mixed Lyra–scalar branch $P_{\beta}$, and various scalar-field–dominated points, showing how viscosity and interaction shape the phase space and late-time behavior. Through an MCMC analysis with Pantheon+ SN, BAO, and SH0ES data, the model parameters are constrained to values that yield a Hubble parameter $h_0$ consistent with local measurements and an energy transfer parameter $\delta$ that supports accelerated expansion without a cosmological constant. Overall, the results suggest that viscous dark energy in Lyra geometry provides a viable and testable extension of standard cosmology, with potential implications for resolving tensions in late-time data and for the dynamical nature of the dark sector.

Abstract

We investigate the cosmological dynamics of a universe described by Lyra's geometry in the presence of dark energy (DE) and dark matter (DM). Dark energy is modeled as a quintessence scalar field with bulk viscosity, while dark matter is allowed to interact with the scalar sector. The displacement vector field, arising naturally in Lyra's manifold, provides an additional geometric contribution. By employing dynamical system techniques, we analyze stability properties and late-time attractors. Our results indicate that viscosity and DE--DM interaction enrich the phase space structure and can help address both the cosmic acceleration and the coincidence problem. Furthermore, by performing a Markov Chain Monte Carlo (MCMC) analysis with recent observational datasets, we derive best-fit values for the model parameters that exhibit good consistency with current data.

Figures (7)

• Figure 1: Phase portrait and corresponding evolution of cosmological parameters for $\gamma=-1, \alpha=1, \delta=0$ with initial values $x(0)=0.18$, $y(0)=0.73$, $\Omega_{\beta}(0)=0.065$, $\Omega_{viscous}(0)=0$. The system evolves toward a Lyra-dominated stable attractor.
• Figure 2: Phase portrait and cosmological evolution for $\gamma=-1, \alpha=1, \delta=0$, $x(0)=0.32$, $y(0)=0.86$, $\Omega_{\beta}(0)=0.065$, $\Omega_{viscous}(0)=0.01$. Weak viscosity leads to damped stable trajectories.
• Figure 3: Phase portrait and parameter evolution for $\gamma=-1, \alpha=1, \delta=0.07$, $x(0)=0.16$, $y(0)=0.81$, $\Omega_{\beta}(0)=0.06$, $\Omega_{viscous}(0)=0$. Weak interaction shifts the stability basin, yielding one stable and one saddle point.
• Figure 4: Phase portrait and cosmological evolution for $\gamma=-1, \alpha=1, \delta=0.07$, $x(0)=0.19$, $y(0)=0.76$, $\Omega_{d}(0)=0.13$, $\Omega_{viscous}(0)=0.01$. Both weak interaction and viscosity yield a globally stable focus-type attractor.
• Figure 5: Phase portrait and corresponding evolution of cosmological parameters for $\gamma = -1$, $\alpha = 1$, $\delta = 0.07$, with assigned initial values $x(0)=0.38$, $y(0)=0.81$, $\Omega_{d}(0)=0.1$, and $\Omega_{viscous}(0)=0.1$. Strong coupling and viscosity enhance damping and alter the basin of attraction.