Seven hints that early-time new physics alone is not sufficient to solve the Hubble tension

The Hubble tension has now grown to a level of significance which can no longer be ignored and calls for a solution which, despite a huge number of attempts, has so far eluded us. Significant efforts in the literature have focused on early-time modifications of $\Lambda$CDM, introducing new physics operating prior to recombination and reducing the sound horizon. In this opinion paper I argue that early-time new physics alone will always fall short of fully solving the Hubble tension. I base my arguments on seven independent hints, related to 1) the ages of the oldest astrophysical objects, 2) considerations on the sound horizon-Hubble constant degeneracy directions in cosmological data, 3) the important role of cosmic chronometers, 4) a number of ``descending trends'' observed in a wide variety of low-redshift datasets, 5) the early integrated Sachs-Wolfe effect as an early-time consistency test of $\Lambda$CDM, 6) early-Universe physics insensitive and uncalibrated cosmic standard constraints on the matter density, and finally 7) equality wavenumber-based constraints on the Hubble constant from galaxy power spectrum measurements. I argue that a promising way forward should ultimately involve a combination of early- and late-time (but non-local -- in a cosmological sense, i.e. at high redshift) new physics, as well as local (i.e. at $z \sim 0$) new physics, and I conclude by providing reflections with regards to potentially interesting models which may also help with the $S_8$ tension.