Cosmographic Analysis in Generalized Rastall-Rainbow Gravity

In this work, we explore a unified gravity framework referred to as Rastall-Rainbow (R-R) gravity, which synthesizes features of Rastall gravity with the energy-dependent spacetime of Rainbow gravity. Within this formulation, we examine the dynamical behavior of a Friedmann-Robertson-Walker (FRW) universe by employing phase-plane techniques. The stability of the system is investigated through trajectories in the (ζ, χ) plane, highlighting conditions under which cosmic evolution remains dynamically consistent. Furthermore, we connect the theory to observationally motivated quantities by reconstructing cosmographic parameters such as the deceleration, jerk, snap, and lerk indices. These diagnostics provide a model-independent description of cosmic kinematics, enabling a deeper understanding of the expansion history in the RR framework. Graphicalanalysis illustrates distinct evolutionary features and possible departures from standard cosmology, suggesting that the unified approach can serve as a viable alternative gravitational model for describing the universes late-time acceleration.