A novel f(R,T) hybrid model for unified dark energy and dark matter dynamics in cosmic evolution

This study investigates the [Formula: see text] gravitational framework by introducing a novel functional form, [Formula: see text], which incorporates power-law and logarithmic dependencies on the trace of the energy-momentum tensor [Formula: see text]. These terms enrich the phenomenological interaction between matter and geometry, enabling a comprehensive exploration of their role in cosmic evolution. We derive the modified field equations and analyze their implications for late-time cosmic acceleration, matter clustering, and the formation of large-scale structures. The model reveals notable deviations from the standard [Formula: see text]CDM cosmology, including distinctive signatures in the matter power spectrum, the Integrated Sachs–Wolfe (ISW) effect, and the anisotropies of the cosmic microwave background (CMB). The parameters [Formula: see text], [Formula: see text], and [Formula: see text] introduce scale-dependent modifications to the gravitational constant [Formula: see text], which influence the growth of structures and the expansion history. These features allow the model to address fundamental cosmological challenges such as the cosmological constant problem and the coincidence problem by dynamically regulating the evolution of dark matter and dark energy densities. We emphasize the potential of this framework to unify dark energy and dark matter dynamics while offering testable predictions for future large-scale cosmological surveys such as Euclid and LSST. The results underscore the versatility of the [Formula: see text] model in explaining the observed universe’s accelerated expansion and the growth of cosmic structures without requiring exotic fields or modifications to General Relativity.