Cosmological quantum tunneling and holographic principle

The probable trajectory of the ground-state wave function of the universe arises through quantum tunneling by gravitational instantons. We calculate the quantum tunneling rate for an $(n{>}2)$-dimensional closed Friedmann–Robertson–Walker universe with a positive cosmological constant. In four dimensions, we use the holographic principle to relate the tunneling rate to the maximal entropy of the early universe after quantum tunneling.