Sound horizon independent constraints on early dark energy: the role of supernova data

We assess the consistency of cosmological models that alter the size of the sound horizon at last scattering to resolve the Hubble tension with data from ACT + Planck CMB lensing, Big Bang Nucleosynthesis, and supernova data from Pantheon or Pantheon+. We use early dark energy (EDE) as an example model but conclude that the results could apply to other similar models. We constrain ΛCDM and EDE with these data finding that while they can constrain ΛCDM very tightly, EDE opens up the parameter space significantly and allows H₀ > 72 km s^-1Mpc^-1. We combine these data with measurements from ACT + Planck TT650TEEE CMB primary anisotropy and galaxy baryon acoustic oscillations, and find that overall, EDE fits these data better than ΛCDM at ≈ 2σ. However, the fit to specifically the sound-horizon-independent measurements is worse for EDE than ΛCDM. We assess this increase in χ ² coming from the sound-horizon-independent measurements and find that the best-fit model is still consistent with a random statistical fluctuation even with H₀ values around 72 km s^-1Mpc^-1.