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

TL;DR

This paper provides a comprehensive comparison of Bayesian and frequentist methods to constrain primordial tensor perturbations using recent cosmological data, emphasizing the impact of statistical approach choices on parameter limits.

Contribution

It introduces a dual-method analysis of tensor parameters, revealing differences in constraints and highlighting the importance of method selection in cosmological parameter estimation.

Findings

Bayesian and frequentist limits on r differ due to prior and volume effects.

Current data do not tightly constrain the tensor spectral tilt n_t.

Largest r values show better agreement between methods.

Abstract

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.