Generalized Holographic Dark Energy Model with Varying C

In this paper we consider a theoretical model for Holographic Dark Energy (HDE) based on the Hubble horizon as a IR cut-off. Our aim is to investigate the evolution of the Generalized Holographic Dark Energy (GHDE) model by varying the parameter C as a function of redshift i. e. C = C(z) in the flat universe of FRW. We have extracted the parameters of the equation of state, fractional dark energy density and deceleration and examined their behavior by plotting each of them in terms of redshift. Our findings show that the GHDE model described in the Hubble length IR cut-off could be a phantom or quintessence in the future. We have also shown that in the past, dark matter was dominant, indicating a slow expansion of the universe. We are currently witnessing a period of dominant dark energy, meaning that the expansion of the universe is accelerating, consistent with observations. Finally, we have shown that in the future depending on the value of the holographic parameter, we may witness a sustained accelerating expansion, a phantom or a Big Rip. In general our analysis shows that by varying the holographic parameter, the Hubble horizon, despite its limitations, can successfully drive late-time cosmic acceleration and exhibit rich phenomenology including phantom and quintessence phases.