Holographic energy density, dark energy sound speed, and tensions in cosmological parameters: $H_0$ and $S_8$

Interesting discrepancies in cosmological parameters are challenging the success of the $\Lambda$CDM model. Direct measurements of the Hubble constant $H_0$ using Cepheid variables and supernovae turn out to be higher than inferred from the Cosmic Microwave Background (CMB). Weak galaxy lensing surveys consistently report values of the strength of matter clustering $\sigma_8$ lower than values derived from the CMB in the context of $\Lambda$CDM. In this paper we address these discrepancies in cosmological parameters by considering Dark Energy (DE) as a fluid with evolving equation of state $w_{\mathrm{de}}(z)$, constant sound speed squared $\hat{c}_{\mathrm{s}}^{2}$, and vanishing anisotropic stress $\sigma$. Our $w_{\mathrm{de}}(z)$ is derived from the Holographic Principle and can consecutively exhibit radiation-like, matter-like, and DE-like behaviour, thus affecting the sound horizon and the comoving angular diameter distance, hence $H_0$. Here we show DE sound speed plays a part in the matter clustering behaviour through its effect on the evolution of the gravitational potential. We compute cosmological constraints using several data set combinations including primary CMB, CMB lensing, redshift-space-distortions, local distance-ladder, supernovae, and baryon acoustic oscillations. In our analysis we marginalise over $\hat{c}_{\mathrm{s}}^{2}$ and find $\hat{c}_{\mathrm{s}}^{2}=1$ is excluded at $\gtrsim 3\sigma$. For our baseline result including the whole data set we found $H_0$ and $\sigma_8$ in good agreement (within $\approx 2\sigma$) with low redshift probes. Our constraint for the baryon energy density $\omega_{\rm{b}}$ is however in $\approx 3\sigma$ tension with BBN constraints. We conclude evolving DE also having non-standard clustering properties [e.g., $\hat{c}_{\mathrm{s}}^{2}(z,k)$] might be relevant for the solution of current discrepancies in cosmological parameters.