Towards alleviating the $H_0$ and $S_8$ tensions with Early Dark Energy - Dark Matter drag

Early dark energy, an additional component of dark energy active in the decade of redshift before recombination, has emerged as one of the most effective models at reducing the $H_0$ tension between direct measurement of the Hubble parameter $H_0$ in the late-universe and the $\Lambda$CDM prediction when calibrated on Planck. However, it requires a slight increase in the dark matter density $\omega_{\rm cdm}$ and primordial tilt $n_s$ that worsens the $S_8$ tension between measurements of weak gravitational lensing at low redshifts and the Planck/$\Lambda$CDM prediction. Using a phenomenological fluid model, we investigate whether the inclusion of a drag term between dark matter and early dark energy can compensate for the effect of the increase in power at small-scales, such that both $H_0$ and $S_8$ tensions are simultaneously alleviated. We find that this works if the drag term is dynamically relevant in the post-recombination universe. However, a drag term active before or just around the time at which the early dark energy contribution to the energy density is maximum is significantly constrained due to its impact on the matter perturbations before recombination, and the subsequent modifications to the cosmic microwave background power spectra.