Updated constraints on amplitude and tilt of the tensor primordial spectrum

Abstract

We have taken a comprehensive approach to update the limits on the tensor-to-scalar ratio ($r$) and the tensor spectral index ($n_t$), using 10 datasets from the BICEP/Keck Array 2015 and 2018, Planck releases 3 and 4, and LIGO-Virgo-KAGRA Collaboration. By fitting the complete $\Lambda$CDM+$r$+$n_t$ model with two different approaches for the tensor sector, we have not only established which method is the most reliable, but have also achieved the strongest constraint on the tensor-to-scalar ratio in current literature: $r<0.028$ and $-1.37<n_t<0.42$ at 95% confidence level. Furthermore, our examination of the common signal detected by the NANOGrav Collaboration further confirms that a simple power-law cannot reconcile the constraints from different datasets if the NANOGrav detection is due to a primordial inflationary gravitational wave background, as previously shown in the literature.

Version coherent with published one. Added new analysis in section 2.4. Added new section 5.1. Added appendix B. Conclusions unchanged

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