TDCOSMO. III. Dark matter substructure meets dark energy. The effects of (sub)halos on strong-lensing measurements of H0

Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant H₀. The lens models used in time delay cosmography omit dark matter subhalos and line-of-sight halos because their effects are assumed to be negligible. We explicitly quantify this assumption by analyzing mock lens systems that include full populations of dark matter subhalos and line-of-sight halos, applying the same modeling assumptions used in the literature to infer H₀. We base the mock lenses on six quadruply imaged quasars that have delivered measurements of the Hubble constant, and quantify the additional uncertainties and/or bias on a lens-by-lens basis. We show that omitting dark substructure does not bias inferences of H₀. However, perturbations from substructure contribute an additional source of random uncertainty in the inferred value of H₀ that scales as the square root of the lensing volume divided by the longest time delay. This additional source of uncertainty, for which we provide a fitting function, ranges from 0.7 - 2.4%. It may need to be incorporated in the error budget as the precision of cosmographic inferences from single lenses improves, and it sets a precision limit on inferences from single lenses.