Constraining holographic dark energy and analyzing cosmological tensions

We investigate cosmological constraints on the holographic dark energy (HDE) using the state-of-the-art cosmological datasets: Planck CMB angular power spectra and weak lensing power spectra, Atacama Cosmology Telescope (ACT) temperature power spectra, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements from six-degree-field galaxy survey and Sloan Digital Sky Survey (DR12 & DR16) and the Cepheids-Supernovae measurement from SH0ES team (R22). We also examine the HDE model and CDM with and without N ₄₅₅ (effective number of relativistic species) being treated as a free parameter. We find that the HDE model can relieve the tensions of H₀ and S₈ to certain degrees. With ``Planck+ACT+BAO+RSD'' datasets, the constraints are H₀ = 69. 70 1. 39\ km\ s^-1 Mpc^{-1} and S₈ = 0. 823 0. 011 in HDE model, which brings down the Hubble tension down to 1. 92 confidence level (C. L. ) and the S₈ tension to 1-2 C. L. By adding the R22 data, their values are improved as H₀ = 71. 86 0. 93 \, km\ s^-1 Mpc^{-1} and S₈ = 0. 813 0. 010, which further brings the Hubble tension down to 0. 85 C. L. and relieves the S₈ tension. We also quantify the goodness-of-fit of different models with Akaike information criterion (AIC) and Bayesian information criterion (BIC), and find that the HDE agrees with the observational data better than the CDM and other extended models (treating N ₄₅₅ as free for fitting).