  An earlier paper points out that a quantum treatment of the string landscape
is necessary. It suggests that the wavefunction of the universe is mobile in
the landscape until the universe reaches a meta-stable site with its
cosmological constant $\Lambda_0$ smaller than the critical value $\Lambda_c$,
where $\Lambda_c$ is estimated to be exponentially small compared to the Planck
scale. Since this site has an exponentially long lifetime, it may well be
today's universe. We investigate specific scenarios based on this quantum
diffusion property of the cosmic landscape and find a plausible scenario for
the early universe. In the last fast tunneling to the $\Lambda_0$
($<\Lambda_c$) site in this scenario, all energies are stored in the nucleation
bubble walls, which are released to radiation only after bubble collisions and
thermalization. So the $\Lambda_0$ site is chosen even if $\Lambda_0$ plus
radiation is larger than $\Lambda_c$, as long as the radiation does not
destabilize the $\Lambda_0$ vacuum. A consequence is that inflation must happen
before this last fast tunneling, so the inflationary scenario that emerges
naturally is extended brane inflation, where the brane motion includes a
combination of rolling, fast tunnelings, slow-roll, hopping and percolation in
the landscape. We point out that, in the brane world, radiation during
nucleosynthesis are mostly on the standard model branes (brane radiation, as
opposed to radiation in the bulk). This distinction may lead to interesting
dynamics. We consider this paper as a road map for future investigations.
