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Two new fast single radio bursts FRB 180924 and FRB 190523 well localized tomassive galaxies have opened a new window to probe and characterize how cosmicbaryons are allocated between galaxies, their surroundings and intergalacticmedium. We are motivated by testing Einstein's weak equivalence principle withthese two cosmic transients which have accurate redshifts. Using photons withdifferent energies emitted by FRB 180924, we obtain, so far, the most stringentbound $\Delta\gamma<2.16\times10^{-10}$ for non-repeating FRBs with accurateredshifts when only considering the gravitational potential of the Milk Way. Ifusing the gravitational potential of the Laniakea supercluster instead of theMilk Way one, we also obtain the strictest bound$\Delta\gamma<1.06\times10^{-14}$ to date. In light of rapid progress of FRBcosmology, towards the next two decades, we give an universal limitation$\Delta\gamma<8.24\times10^{-22}$ from photons with different energies emittedby single FRBs with accurate redshifts. Moreover, we analyze detailedly theeffects of various astrophysical parameters on the precision of weakequivalence principle. We also estimate the abilities of single FRBs with knownredshifts to test the validity of swampland criterion, and to distinguish whichvalue of $H_0$ is preferred.

Weak equivalence principle, swampland and $H_0$ tension with fast single radio bursts FRB 180924 and FRB 190523