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Upcoming measurements of the small-scale primary cosmic microwave background(CMB) temperature and polarization power spectra ($TT$/$TE$/$EE$) areanticipated to yield transformative constraints on new physics, including theeffective number of relativistic species in the early universe ($N_{\rm eff}$).However, at multipoles $\ell \gtrsim 3000$, the primary CMB power spectrareceive significant contributions from gravitational lensing. While these modesstill carry primordial information, their theoretical modeling requiresknowledge of the CMB lensing convergence power spectrum, $C_L^{\kappa\kappa}$,including on small scales where it is affected by nonlinear gravitationalevolution and baryonic feedback processes. Thus, the high-$\ell$ primary CMB issensitive to these late-time, nonlinear effects. Here, we show thatinaccuracies in the modeling of $C_L^{\kappa\kappa}$ can yield surprisinglylarge biases on cosmological parameters inferred from the primary CMB powerspectra measured by the upcoming Simons Observatory and CMB-S4 experiments. ForCMB-S4, the biases can be as large as $1.6\sigma$ on the Hubble constant $H_0$in a fit to $\Lambda$CDM and $1.2\sigma$ on $N_{\rm eff}$ in a fit to$\Lambda$CDM+$N_{\rm eff}$.  We show that these biases can be mitigated by explicitly discarding all $TT$data at $\ell>3000$ or by marginalizing over parameters describing baryonicfeedback processes, both at the cost of slightly larger error bars. We alsodiscuss an alternative, data-driven mitigation strategy based on delensing theCMB $T$ and $E$-mode maps. Finally, we show that analyses of upcoming data willrequire Einstein-Boltzmann codes to be run with much higher numerical precisionsettings than is currently standard, so as to avoid similar -- or larger --parameter biases due to inaccurate theoretical predictions.

Baryonic feedback biases on fundamental physics from lensed CMB power spectra