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In this paper, a stable flat cosmological model has been constructed and theevolution of dark energy has been investigated in the framework of the recentlysuggested $\kappa(R,T)$ gravity. The empirical approach we adopt in the currentwork reveals some interesting cosmological features consistent withobservations and the standard $\Lambda$CDM model. The evolution of cosmicpressure shows a positive-to-negative transition corresponding to the cosmicdeceleration-acceleration transition, both the deceleration parameter and thecosmic pressure have the positive-to-negative sign flipping. While thisbehavior can provide explanation for the deceleration-acceleration transition,the reason behind this positive-negative transition itself is still missing.

Probing $\kappa(R,T)$ cosmology via empirical approach