Path Integral Complexity and Kasner singularities

Understand

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.