  The injection of early dark energy (EDE) before the recombination, a possible
resolution of the Hubble tension, will not only shift the scalar spectral index
$n_s$ towards $n_s=1$, but also be likely to tighten the current upper limit on
tensor-to-scalar ratio $r$. In this work, with the latest CMB datasets (Planck
PR4, ACT, SPT and BICEP/Keck), as well as BAO and SN, we confirm this result,
and discuss its implication on inflation. We also show that if we happen to
live with EDE, how the different inflation models currently allowed would be
distinguished by planned CMB observations, such as CMB-S4 and LiteBIRD.
