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Motivated by the swampland program, we show that the Weil-Petersson geometryof the moduli space of a Calabi-Yau manifold of complex dimension $d\leq4$ is agravitational instanton (i.e. a finite-action solution of the Euclideanequations of motion of gravity with matter). More precisely, the moduligeometry of Calabi-Yau $d$-folds ($d\leq4$) describes instantons of (E)AdSEinstein gravity coupled to a standard chiral model.  From the point of view of the low-energy physics of string/M-theorycompactified on the Calabi-Yau $X$, the various fields propagating on itsmoduli space are the couplings appearing in the effective Lagrangian$\mathscr{L}_\text{eff}$.

Moduli spaces of Calabi-Yau $d$-folds as gravitational-chiral instantons