  We present a concrete holographic realization of the eternal inflation and
its census taker in (1+1) dimensional Liouville gravity by applying the FRW/CFT
philosophy proposed by Freivogel, Sekino, Susskind and Yeh (FSSY). The dual
boundary theory is nothing but the old matrix model describing the
two-dimensional Liouville gravity coupled with minimal model matter fields. In
Liouville gravity, the flat Minkowski space or even the AdS space will decay
into the dS space, which is in stark contrast with higher dimensional theories,
but the spirit of the FSSY conjecture applies with only minimal modification.
We investigate the classical geometry as well as some correlation functions to
support our claim. We also study an analytic continuation to the time-like
Liouville theory to discuss possible applications in (1+3) dimensional
cosmology along with the original FSSY conjecture, where the boundary theory
involves the time-like Liouville theory. We show that the decay rate in the
(1+3) dimension is more suppressed due to the quantum gravity correction of the
boundary theory.
