Determining the Hubble constant without the sound horizon scale: measurements from CMB lensing

ABSTRACT Measurements of the Hubble constant, H0, from the cosmic distance ladder are currently in tension with the value inferred from Planck observations of the cosmic microwave background (CMB) and other high-redshift data sets if a flat Λ cold dark matter (ΛCDM) cosmological model is assumed. One of the few promising theoretical resolutions of this tension is to invoke new physics that changes the sound horizon scale in the early Universe; this can bring CMB and baryon acoustic oscillations (BAO) constraints on H0 into better agreement with local measurements. In this paper, we discuss how a measurement of the Hubble constant can be made from the CMB without using information from the sound horizon scale, rs. In particular, we show how measurements of the CMB lensing power spectrum can place interesting constraints on H0 when combined with measurements of either supernovae or galaxy weak lensing, which constrain the matter density parameter. The constraints arise from the sensitivity of the CMB lensing power spectrum to the horizon scale at matter–radiation equality (in projection) ; this scale could have a different dependence on new physics than the sound horizon. From an analysis of current CMB lensing data from Planck and Pantheon supernovae with conservative external priors, we derive an rs-independent constraint of H₀ = 73. 5 5. 3\, km\, s^-1\, Mpc^-1. Forecasts for future CMB surveys indicate that improving constraints beyond an error of (H₀) = 3\, km\, s^-1\, Mpc^-1 will be difficult with CMB lensing, although applying similar methods to the galaxy power spectrum may allow for further improvements.