Late-time data require smaller sound horizon at recombination

The Hubble constant problem is that the values of Hubble constant from the observation of cosmic microwave background assuming the LambdaCDM model disagrees with the values from direct measurements. This problem suggests some new physics beyond the LambdaCDM model. Typically there are two ways of reconciliation: one is the realization of smaller value of sound horizon at recombination, and the other is the modification of the way of expansion of the universe after recombination. In this letter we examine the latter possibility by comparing two typical phenomenological dark energy models with the distance-redshift relation provided by Pantheon catalogue of supernova observations and galaxy surveys by BOSS and eBOSS collaborations. Though these phenomenological dark energy models globally fit observations better than the LambdaCDM model, they are strongly disfavored by the distance-redshift relation as almost the same level as the LambdaCDM model defined by cosmic microwave background observations. The distance-redshift relation strongly suggests some new physics which realize smaller value of sound horizon at recombination.