# Optimistic estimation on probing primordial gravitational waves with CMB B-mode polarization

## TL;DR

This paper assesses the potential to detect primordial gravitational waves through CMB B-mode polarization measurements, considering theoretical inflation models and cosmic variance limitations, without relying on multi-frequency data.

## Contribution

It provides an optimistic sensitivity estimate for detecting primordial gravitational waves using only CMB B-modes, analyzing the impact of cosmic variance and inflation model predictions.

## Key findings

- Detection thresholds for tensor-to-scalar ratio r are close to inflation model predictions.
- Cosmic variance limits the measurement of the tensor spectral index n_t.
- The canonical single-field slow-roll inflation relation n_t = -r/8 cannot be distinguished from scale invariance.

## Abstract

In the measurements of cosmic microwave background polarizations, three frequency channels are necessary for discriminating the primordial B-modes from the polarized dust and the synchrotron emission. We carry out an optimistic estimate on the sensitivity to the detection of primordial gravitational waves using the cosmic microwave background B-modes only, and explore how to reach the thresholds for the tensor-to-scalar ratio $r$ in the theoretically well-motivated inflation models. For example, Lyth bound implies $r \simeq 2\times10^{-3}$, a corrected Lyth bound shows $r \simeq 7\times10^{-4}$, and some typical inflation models gives $r\simeq4\times10^{-5}$. Taking into account the up-to-date constraints on $r$, i.e. $r_{0.05}<0.07$ at $95\%$ confidence, we find that the consistency relation $n_t=-r/8$ in the canonical single-field slow-roll inflation cannot be distinguished from the scale invariance, due to the cosmic variance in the power spectrum of cosmic microwave background B-modes. The cosmic variance places an inevitable limit on the measurements of the tensor spectral index, i.e. $\sigma_{n_t}\simeq0.01$ for $2\leqslant\ell\leqslant \ell_\text{max}=300$.