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We discuss the phenomenological imprints of modifications to gravity in the early Universe with a specific focus on the time of recombination. We derive several interesting results regarding the effect that such modifications have on cosmological observables, especially on the driving and phasing of acoustic oscillations, observed in the cosmic microwave background (CMB) and baryon acoustic oscillations, as well as the weak gravitational lensing of the CMB and of galaxy shapes. This widens the pool of measurements that can be used to test gravity with present and future surveys, in particular realizing the full constraining power of the structure of the primary peaks of the CMB spectrum. We investigate whether such a phenomenology can relax tensions between cosmological measurements and find that a modification of the gravitational constant at recombination would help in reconciling measurements of the CMB with local measurements of the Hubble constant.
Lin et al. (Tue,) studied this question.