Attractor solutions in an interacting quintessence with varying-mass dark matter in Lyra's geometry.

In background dynamics of a spatially flat FLRW model of the universe, we investigate an interacting scenario of quintessence scalar field as dark energy which interacts with pressure-less dust as dark matter, mass of which varies with time through scalar field in context of Lyra's geometry. Mass of dark matter particles and the potential of the quintessence field are considered to be functions depending exponentially on scalar field. Cosmological evolution equations in this context are converted into an autonomous system of ordinary differential equations by suitable transformation of the cosmological variables into dimensionless dynamical variables and the nature of critical points are found by applying linear stability theory. We have obtained cosmologically interested critical points which describe the attractor solutions at late times. Some of which representing the accelerated scalar field-dark matter scaling solutions in attractor regime with similar order of energy densities can provide the possible solution of the coincidence problem.