Can Holographic dark energy models fit the observational data?

In this work we investigate the holographic dark energy models with slowly time-varying model parameter defined based on the current Hubble horizon length scale. While the previous studies on the three popular holographic dark energy models defined based on the future event horizon, Ricci scale and Granda-Oliveros IR cutoffs showed that these models cannot fit the observational data [1], in this work we show that the holographic dark energy models with time-varying model parameter defined on the current Hubble radius are well favored by observations. Using the standard $\chi^2$ minimization in the context of Markov Chain Monte Carlo method, we compare the ability of holographic dark energy models with time-varying $c^2$ parameter constructed on the current Hubble length scale against different sets of observational data namely expansion data, growth rate data and expansion+growth rate data respectively. Based on the values of Akaike and Bayesian information criteria, we find that these types of holographic dark energy models are well fitted to both expansion and growth rate observations as equal to $\Lambda$CDM cosmology. We also put constraints on the cosmological parameters and show that the transition epoch form early decelerated to current accelerated expansion calculated in holographic dark energy models with time-varying model parameter defined on the Hubble length is consistent with observations.