Bayesian evidence against the Harrison-Zel’dovich spectrum in tensions with cosmological data sets

Current cosmological constraints on the scalar spectral index of primordial fluctuations n_s in the ΛVcold dark matter (ΛCDM) model have excluded the minimal scale-invariant Harrison-Zel’dovich model (n_s=1; hereafter HZ) at high significance, providing support for inflation. In recent years, however, some tensions have emerged between different cosmological data sets that, if not due to systematics, could indicate the presence of new physics beyond the ΛCDM
model. In light of these developments, we evaluate the Bayesian evidence against HZ in different data combinations and model extensions. Considering only the Planck temperature data, we find inconclusive evidence against HZ when including variations in the neutrino number N_eff and/or the helium abundance 
Y_He. Adding the Planck polarization data, on the other hand, yields strong evidence against HZ in the extensions we considered. Perhaps most interestingly, Planck temperature data combined with local measurements of the Hubble parameter [A. G. Riess et al., Astrophys. J. 826, 56 (2016); A. G. Riess et al. Astrophys. J. 861, 126 (2018)] give as the most probable model a HZ spectrum, with additional neutrinos. However, with the inclusion of polarization, standard ΛCDM is once again preferred, but the HZ model with extra neutrinos is not strongly disfavored. The possibility of fully ruling out the HZ spectrum is therefore ultimately connected with the solution to current tensions between cosmological data sets. If these tensions are confirmed by future data, then new physical mechanisms could be at work and a HZ spectrum could still offer a valid alternative.