Possible resolution of the Hubble tension with Weyl invariant gravity

We explore cosmological implications of a genuinely Weyl invariant (WI) gravitational interaction. The latter reduces to general relativity in particular conformal frame for which the coupling and active masses are fixed. Specifically, we consider model this framework that is {\it dynamically} identical standard (SM) cosmology. However, kinematics} test particles traveling new background metric modified thanks (cosmological) fundamental mass scale, $\gamma$, model. Since lapse-function radially-dependent any incoming photon experiences (gravitational) red/blueshift comoving} frame, unlike SM. Distance scales as well due scale $\gamma$. claimed $4.4\sigma$ tension level between locally measured Hubble constant, $H_{0}$, with SH0ES corresponding value inferred from cosmic microwave (CMB) could then be significantly alleviated by an earlier-than-thought recombination. Assuming vanishing spatial curvature, either one Planck 2018 (P18) or dark energy survey (DES) yr1 data sets subject prior imply $\gamma^{-1}$ $O(100)$ times larger than $H_{0}^{-1}$. Considering P18+SH0ES P18+DES+SH0ES set combinations, odds against $\gamma$ over 1000:1 2000:1, respectively, strongly favored SM deviance information criterion (DIC) gain $\gtrsim 10$ 12$, respectively. reduced $\sim 1.5$ $1.3 \sigma$, conclude $H_{0}$ may simply result yet unrecognized symmetry interaction -- invariance. (abridged)