Cosmological Evolution of the Randall-Sundrum II Model with Running Vacuum: A Special Class of Solutions

Abstract

In this work, we construct a novel cosmological framework by integrating the running vacuum model into the Randall-Sundrum II braneworld scenario. We derive a special class of analytical solutions in the model. Our investigation focuses on the complete evolutionary trajectory of the universe, with particular emphasis on the realization of primordial inflation and the evolution of cosmic entropy. We evaluate the model's viability across three scenarios: dust-dominated, radiation-dominated, and general perfect fluid-dominated universes. Our findings show that while the hybrid model is in principle capable of supporting inflation, producing enough e-fold number demands either severe fine-tuning of the parameter or unreasonably large (and thus physically unnatural) value of the parameter.