Toward inflation with ns=1 in light of the Hubble tension and implications for primordial gravitational waves

Abstract

Recently, it has been found that complete resolution of the Hubble tension might point to a scale-invariant Harrison-Zeldovich spectrum of primordial scalar perturbation, i.e., ${n}_{s}=1$ for ${H}_{0}\ensuremath{\sim}73\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. We show that, for well-known slow-roll models, if inflation ends by a waterfall instability with respect to another field in the field space while inflaton is still at a deep slow-roll region, then ${n}_{s}$ can be lifted to ${n}_{s}=1$. A surprise of our result is that with prerecombination early dark energy, chaotic ${\ensuremath{\phi}}^{2}$ inflation, strongly disfavored by $\mathrm{Planck}+\mathrm{BICEP}/\mathrm{Keck}$ in standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, can be revived, which is now well within testable region of upcoming cosmic microwave background B-mode experiments.