Path Integral Complexity and Kasner singularities

We explore properties of path integral complexity in field theories on time dependent backgrounds using its dual description in terms of Hartle-Hawking wavefunctions. In particular, we consider boundary theories with time dependent couplings which are dual to Kasner-AdS metrics in the bulk with a time dependent dilaton. We show that holographic path integral complexity decreases as we approach the singularity, consistent with earlier results from holographic complexity conjectures. Furthermore, we find examples where the complexity becomes universal i.e., independent of the Kasner exponents, but the properties of the path integral tensor networks depend sensitively on this data.

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