Robust constraints on tensor perturbations from cosmological data: a comparative analysis from Bayesian and frequentist perspectives

We analyze primordial tensor perturbations using the latest cosmic microwave background and gravitational waves data, focusing on the tensor-to-scalar ratio, $r$, and the tensor spectral tilt, $n_t$. Utilizing data from Planck PR4, BICEP/Keck, and LIGO-Virgo-KAGRA, we employ both Bayesian and frequentist methods to provide robust constraints on these parameters. Our results indicate more conservative upper limits for $r$ with profile likelihoods compared to Bayesian credible intervals, highlighting the influence of prior selection and volume effects. The profile likelihood for $n_t$ shows that the current data do not provide sufficient information to derive quantitative bounds, unless extra assumptions on $r$ are used. Additionally, we conduct a 2D profile likelihood analysis of $r$ and $n_t$, indicating a closer agreement between both statistical methods for the largest values of $r$. This study not only updates our understanding of the tensor perturbations but also highlights the importance of employing both statistical methods to explore less constrained parameters, crucial for future explorations in cosmology.