Inflation Model Selection meets Dark Radiation

We investigate how inflation model selection is affected by the presence of additional free-streaming relativistic degrees of freedom, i.e. dark radiation. We perform a full Bayesian analysis of both inflation parameters and cosmological parameters taking reheating into account self-consistently. We compute the Bayesian evidence for a few representative inflation scenarios in both the standard $\Lambda$CDM model and an extension including dark radiation parametrised by its effective number of relativistic species $N_\mathrm{eff}$. Using a minimal dataset (Planck low-$\ell$ polarisation, temperature power spectrum and lensing reconstruction), we find that the observational status of most inflationary models is unchanged. The exceptions are potentials such as power-law inflation that predict large values for the scalar spectral index that can only be realised when $N_\mathrm{eff}$ is allowed to vary. Adding baryon acoustic oscillations data and the B-mode data from BICEP2/Keck makes power-law inflation disfavoured, while adding local measurements of the Hubble constant $H_0$ makes power-law inflation slightly favoured compared to the best single-field plateau potentials. This illustrates how the dark radiation solution to the $H_0$ tension would have deep consequences for inflation model selection.