4D Gauss-Bonnet gravity: cosmological constraints, $H_0$ tension and large scale structure

We perform correct and reasonable cosmological constraints on the newly proposed 4D Gauss-Bonnet gravity. Using the joint constraint from cosmic microwave background, baryon acoustic oscillations, Type Ia supernovae, cosmic chronometers and redshift space distortions, we obtain, so far, the strongest constraint $\tilde{\alpha}=(1.2\pm5.2)\times 10^{-17}$, namely $\alpha=(2.69\pm11.67)\times10^{48}$ eV$^{-2}$, among various observational limitations from different information channels, which is tighter than previous bound from the speed of gravitational wave by at least one order of magnitude. We find that our bound is well supported by the observations of temperature and lensing potential power spectra of cosmic microwave background from the Planck-2018 final release. Very interestingly, the large $H_0$ tension between the local measurement from the Hubble Space Telescope and global derivation from the Planck-2018 final data under the assumption of $\Lambda$CDM can be greatly resolved from $4.4\sigma$ to $1.94\sigma$ level in the 4D Gauss-Bonnet gravity. In theory, we find that this model can partly relieve the coincidence problem and the rescaling Gauss-Bonnet term, which needs the help of the cosmological constant to explain current cosmic acceleration, is unable to serve as dark energy alone.