Quantum Transitions Between Minkowski and de Sitter Spacetimes
  Quantum transitions among de Sitter and Minkowski spacetimes through bubble
nucleation are revisited using the Hamiltonian formalism. We interpret
tunnelling probabilities as relative probabilities: the ratio of the squared
wave functionals
$\mathcal{P}=\frac{|\Psi_{\mathcal{N}}|^2}{|\Psi_{\mathcal{B}}|^2}$, with
$\Psi_{\mathcal{B,N}}$ solutions of the Wheeler-DeWitt equation corresponding
to the spacetimes $\mathcal{N}$ and $\mathcal{B}$, gives the probability of
nucleating the state $\mathcal{N}$ relative to the probability of having the
state $\mathcal{B}$. We find that the transition amplitude from de Sitter to de
Sitter for both up- and down-tunnelling agrees with the original result based
on Euclidean instanton methods. Expanding on the work of Fischler, Morgan and
Polchinski we find that the Minkowski to de Sitter transition is possible as in
the original Euclidean approach of Farhi, Guth and Guven. We further generalise
existing calculations by computing the wave function away from the turning
points for the classical motion of the wall in de Sitter to de Sitter
transitions. We address several challenges for the viability of the Minkowski
to de Sitter transition, including consistency with detailed balance and
AdS/CFT. This sets this transition on firmer grounds but opens further
questions. Our arguments also validate the Coleman-De Luccia formulae in the
presence of gravity since it has no issues involving negative eigenmodes and
other ambiguities of the Euclidean approach. We briefly discuss the
implications of our results for early universe cosmology and the string
landscape.
