Qualitative study of Lyra cosmologies with spatial curvature

Abstract

We investigate the spatially curved Friedmann–Robertson–Walker space–time with Lyra geometry model. The cosmological solutions are studied by using dynamical system methodology to explore the universe evolution in the model. The constructed autonomous system has been explored to extract the physically viable cosmological solutions by studying the behavior of eigenvalues at the fixed points of the system. Late-time attractor solution corresponding to the accelerated expansion exist in the model and thus, the model may explain the late-time accelerating expansion of universe. The model is also composed of deceleration to acceleration transition with Λ cold dark matter evolution at late-times. The evolution of cosmological parameters like deceleration parameter , effective equation of state parameter, total matter density and role of energy conditions with scale factor have been studied along with statefinder diagnostic to explain the universe evolution in the model. By dynamical system analysis, it has been observed that the displacement field plays a dominant role during the early times and, the universe is dominated by stiff matter like component. Implications of bouncing behavior in the model with role of energy conditions and continuity equation have been discussed in detail along with their physical consequences. • Lyra geometry model with FRW metric having spatial curvature is investigated. • Dynamical system method has been used to extract the cosmic dynamics of model. • The model explains late-time accelerating evolution of universe. • Cosmological parameters are studied by integrating the dynamical variables. • We illustrate that the fixed point corresponding to radiation phase is absent.