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.