New Constraint on the Tensor-to-scalar Ratio from the Planck and BICEP/Keck Array Data Using the Profile Likelihood

Motivated by the discrepancy between Bayesian and frequentist upper limits on the tensor-to-scalar ratio parameter r found by the SPIDER collaboration, we investigate whether a similar trend is also present in the latest Planck and BICEP/Keck Array data. We derive a new upper bound on r using the frequentist profile likelihood method. We vary all the relevant cosmological parameters of the ΛCDM model, as well as the nuisance parameters. Unlike the Bayesian analysis using Markov Chain Monte Carlo (MCMC), our analysis is independent of the choice of priors. Using Planck Public Release 4, BICEP/Keck Array 2018, Planck cosmic microwave background lensing, and baryon acoustic oscillation data, we find an upper limit of r < 0.037 at 95% Confidence Level (C.L.), similar to the Bayesian MCMC result of r < 0.038 for a flat prior on r and a conditioned Planck lowlEB covariance matrix.