Return of Harrison–Zeldovich spectrum in light of recent cosmological tensions

ABSTRACT The spectral index ns of scalar perturbation is the significant initial condition set by inflation theory for our observable Universe. According to Planck results, current constraint is ns = 0.965 ± 0.004, while an exact scale-invariant Harrison–Zeldovich spectrum, i.e. ns = 1, has been ruled out at 8.4σ significance level. However, it is well-known that the standard Lambda cold dark matter model is suffering from the Hubble tension, which is at ∼5σ significance level. This inconsistency likely indicates that the comoving sound horizon at last scattering surface is actually lower than expected, which so seems to be calling for the return of ns = 1. Here, in light of recent observations we find strong evidence for a ns = 1 universe. And we show that if so, it would be confirmed conclusively by CMB-S4 experiment.