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 axionlike particle with quartic self-interactions. These interactions are incorporated into the Einstein–Boltzmann equations using the relaxation time approximation and implemented in the 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 Simons Observatory and the satellite missions LiteBIRD and Probe of Inflation and Cosmic Origins. 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.

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• Cosmic microwave background
• Cosmological parameters
• Gravitational waves