Holographic ComputationalComplexity as a measure for theMultiverse

The landscape of solutions in String Theory leads to the possibility of di�erent universes with its own physical laws and fundamental constants (like cosmological constant(cc), rank of gauge groups and so on). Also, in cosmology, the process of in ation becomes eternal once quantum uctuations are taken into account and gives rise to many universes. Thus, it is plausible that the various distinct string vacua landscape are populating the di�erent pocket universes of the in ationary multiverse. It is hard to de�ne probabilities in the multiverse. In a new approach for multiverse analysis [9] , the multiverse is taken as a simulation by a quantum supercomputer, and the time taken for simulation is the computational complexity. Universes which have less complexity are produced more easily and are common. A recent conjecture by Susskind [10], relates the computational complexity to the Einstein-Hilbert action. The aim of this project is to compute the complexity for a multiverse with two vacua , a pure dS spacetime separated by a domain wall from a Schwarshild AdS spacetime. Di�erent domain wall trajectories are possible. We compute the Einstein-Hilbert action term of this system for the case when the de Sitter radius is less than the black hole event horizon radius.