Recent observational data seem to show $\gtrsim 3\sigma$ evidence for an evolving dark energy (DE) against the cosmological constant, so the standard $\mathrm{\Lambda }$ Cold Dark Matter ($\mathrm{\Lambda }\mathrm{CDM}$) model. In this paper, we perform the search for the primordial gravitational waves with the potential prerecombination solutions to the Hubble tension, using recent DESI baryon acoustic oscillation measurements combined with BICEP/Keck cosmic microwave background (CMB) B-mode polarization, Planck CMB, and Pantheon supernova data, which reveal that the low bound of the tensor-to-scalar ratio $r$ is $>1.5\sigma$ nonzero with the best fit $r_{0.05}\sim 0.01$ and the scalar spectral index $n_s=1$ (both $|r_{0.05}-0.01|$ and $|n_s-1|\sim \mathcal{O}(0.001)$). In particular, we observe the unnoticed impact of CMB B-mode polarization data for constraining the nature of DE, which together with early dark energy solutions to the Hubble tension is calling for the return of postrecombination $\mathrm{\Lambda }\mathrm{CDM}$.

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• Cosmic microwave background
• Cosmological parameters
• Dark energy
• Gravitational waves