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We study the geometry of Euclidean instantons in loop quantum cosmology (LQC)such as those relevant for the no-boundary proposal. Confining ourselves to thesimplest case of a cosmological constant in minisuperspace cosmologies, weanalyze solutions of the semiclassical (Euclidean) path integral in LQC. Wefind that the geometry of LQC instantons have the peculiar feature of aninfinite tail which distinguishes them from Einstein gravity. Moreover, due toquantum-geometry corrections, the small-a behaviour of these instantons seem tonaturally favor a closing-off of the geometry in a regular fashion as wasoriginally proposed for the no-boundary wavefunction.

On the geometry of no-boundary instantons in loop quantum cosmology