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

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.