Bias in the tensor-to-scalar ratio from self-interacting dark radiation

We investigate the cosmological imprint of self-interacting dark radiation (DR) on the primordial $B$-mode angular power spectrum and its impact on the estimation of the tensor-to-scalar ratio $r$. We consider a minimal model in which DR is described as an effectively massless axion-like particle with quartic self-interactions. These interactions are incorporated into the Einstein-Boltzmann equations using the relaxation time approximation and implemented in the $\texttt{CLASS}$ code. We show that increasing the strength of DR self-interactions suppresses anisotropic stress, thereby reducing the damping of gravitational waves and leading to an enhancement of the primordial $B$-mode signal relative to the free-streaming case. Using mock CMB data and Markov Chain Monte Carlo analyses, we show that neglecting DR self-interactions may bias the inferred value of $r$ by an amount comparable to the uncertainty expected in forthcoming CMB polarization experiments, such as the ground-based $\textit{Simons Observatory}$ and the satellite missions $\textit{LiteBIRD}$ and PICO. Our results emphasize the importance of properly modeling DR interactions in future precision searches for primordial $B$-modes in order to obtain unbiased constraints on inflationary gravitational waves.