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In this presentation, we first describe the Hartle-Hawking wave function inthe Euclidean path integral approach. After we introduce perturbations to thebackground instanton solution, following the formalism developed byHalliwell-Hawking and Laflamme, one can obtain the scale-invariant powerspectrum for small-scales. We further emphasize that the Hartle-Hawking wavefunction can explain the large-scale power suppression by choosing suitablepotential parameters, where this will be a possible window to confirm orfalsify models of quantum cosmology. Finally, we further comment on possiblefuture applications, e.g., Euclidean wormholes, which can result in distinctsignatures to the power spectrum.

Hartle-Hawking wave function and large-scale power suppression of CMB