Constrained Dynamics of Holographic Dark Energy in Modified f (R) Gravity

In the present work, we examine the dynamical behaviour of holographic dark energy (HDE) within the framework of modified f(R) gravity in a hypersurface-homogeneous space-time. To explore the universe's evolutionary behaviour under the influence of dark energy, we consider both exponential and power-law expansions. The cosmic evolution is analysed using standard cosmological diagnostics, including the density parameter and equation of state (EoS) parameter along with the deceleration parameter. Furthermore, the statefinder diagnostic pair is tested to detect precisely different phases of the universe. The squared speed of sound parameter was used to incorporate the stability analysis for our models. This investigation links the principles of quantum gravity to cosmology, producing testable predictions for forthcoming research and illustrating that HDE functions as a credible alternative to ΛCDM.