Wormholes in finite cutoff JT gravity: a study of baby universes and (Krylov) complexity

In this paper, as an application of the `Complexity = Volume' proposal, we calculate the growth of the interior of a black hole at late times for finite cutoff JT gravity. Due to this integrable, irrelevant deformation, the spectral properties are modified non-trivially. The Einstein-Rosen Bridge (ERB) length saturates faster than pure JT gravity. We comment on the possible connection between Krylov Complexity and ERB length for deformed theory. Apart from this, we calculate the emission probability of baby universes for the deformed theory and make remarks on its implications for the ramp of the Spectral Form Factor. Finally, we compute the correction to the volume of the moduli space due to the non-perturbative change of the spectral curve because of the finite cutoff at the boundary.