Testing $n_s=1$ in light of the latest ACT and SPT data

It is commonly recognized that the primordial scalar spectral index $n_s$ is approximately $0.96-0.975$, depending on the dataset. However, this view is being completely altered by the early dark energy (EDE) resolutions of the Hubble tension, known as the most prominent tension the standard $\Lambda$CDM model is suffering from. In corresponding models with pre-recombination EDE, resolving the Hubble tension (i.e., achieving $H_0\sim 73$km/s/Mpc) must be accompanied by a shift of $n_s$ towards unity to maintain consistency with the cosmological data, which thus implies a scale invariant Harrison-Zel'dovich spectrum with $n_s=1$ $(|n_s-1|\simeq {\cal O}(0.001))$. In this work, we strengthen and reconfirm this result with the latest ground-based CMB data from ACT DR6 and SPT-3G D1, the precise measurements at high multipoles beyond the Planck angular resolution and sensitivity. Our work again highlights the importance of re-examining our understanding on the very early Universe within the broader context of cosmological tensions.