Constraints on Scalar Spectral Index from Latest Observational Measurements

Abstract With the nine-year data release of the Wilkinson Microwave Anisotropy Probe (WMAP9), it is found that the inflationary models with the scalar spectral index n s ≥ 1 are excluded at about 5 σ confidence level. In this paper, we set the new limits on the scalar spectral index in different cosmological models by the WMAP9 data, the small-scale cosmic microwave background (CMB) measurement from the South Pole Telescope, baryon acoustic oscillation data, Hubble Telescope measurements of the Hubble constant, and supernovae luminosity distance data. In most of extended cosmological models, e.g. with a dark energy equation of state, the constraints on n s do not change significantly, when comparing with that obtained in the standard ΛCDM model. The Harrison–Zel’dovich–Peebles (HZ) scale invariant spectrum is still disfavored at more than 4 σ confidence level. However, when considering the model with an effective number of neutrinos N eff , we obtain the limit on the spectral index of n s = 0.980 ± 0.011 (1 σ ), due to the strong degeneracy between n s and N eff . The HZ spectrum now is consistent with the current data at 95% confidence level. Recently, the Planck collaboration has published CMB maps with the highest precision. Therefore, we also analyze these extended cosmological models again using the Planck data, and find that the degeneracy between n s and N eff still weakens the constraint on the spectral index significantly.