Why reducing the cosmic sound horizon alone cannot fully resolve the Hubble tension

The mismatch between the locally measured expansion rate of the universe and the one inferred from the Planck CMB data within ΛCDM, known as the Hubble tension, has motivated many proposed extensions to ΛCDM that reduce the sound horizon at recombination r_s (e.g., early dark energy, modified neutrino sector, extra radiation, primordial magnetic fields, varying constants). We show that any model which only reduces r_s cannot fully resolve the Hubble tension while remaining consistent with other datasets. Specifically, models that raise H0 with lower Ω_m h^2 are in tension with BAO, while those requiring higher Ω_m h^2 become inconsistent with galaxy weak lensing data.

Karsten Jedamzik, Levon Pogosian, Gong-Bo Zhao