Updated constraints on amplitude and tilt of the tensor primordial spectrum

We have taken a comprehensive approach to update the limits on the tensor-to -scalar ratio (r) and the tensor spectral index (nt), 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 ACDM+r+nt 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 < nt < 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.