Scale-dependence in $Λ$CDM parameters inferred from the CMB: a possible sign of Early Dark Energy

Abstract: The early dark energy (EDE) model is one of the promising solutions to the Hubble tension. One of the successes of the EDE model is that it can provide a similar fit to the $\Lambda$CDM model for the CMB power spectrum. In this work, I analyze the phenomenology of the EDE and $\Lambda$CDM parameters on the CMB temperature power spectrum and notice that this cannot hold on all scales. Thus, if the real cosmology is as described by the EDE model, the $\Lambda$CDM parameters will be scale-dependent when fitting the CMB power spectrum with the $\Lambda$CDM model, which can be hints for the EDE model. I examine CMB-S4-like observations through mock data analysis and find that parameter shifts are notable. As observations include smaller scales, I find lower $H_0$, $n_s$, $\omega_b$ and higher $\omega_m$, $A_s e^{-2\tau}$, which will also constitute new tensions with other observations. They can serve as a possible signal for the EDE model.