Hint of $r\simeq 0.01$ after DESI DR2 ?

In the report by BICEP/Keck collaborations, the tensor-to-scalar ratio is $r_{0.05}<0.036$ (95\% C.L.). However, recent datasets have preferred the evolving dark energy, which thus have significantly shifted the bestfit values of standard $\Lambda$CDM cosmological parameters. In this paper, we perform the joint analysis of BICEP/Keck cosmic microwave background (CMB) B-mode data, latest DESI DR2 baryon acoustic oscillations and supernova data, combined with Planck PR3 and PR4 CMB data respectively, and find $r_{0.05}=0.0159^{+0.0057}_{-0.014}$ and $r_{0.05}=0.0164^{+0.0063}_{-0.014}$. The constraints on $r$ are further tightened compared to the result of BICEP/Keck collaborations. Though there might be still systematic uncertainties in B-mode measurements due to the foreground contamination, our work is to not say what the value of $r$ is, but present the state-of-the-art constraints on $r$ and emphasize that the detection for $r$ depends potentially on our insight into the dark universe, highlighting the important role of cosmological surveys in comprehending our very early universe.