Quantum Transitions Between Minkowski and de Sitter Spacetimes

Abstract

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 P=false|normalΨscriptNfalse|2false|normalΨscriptBfalse|2, with ΨscriptB,scriptN solutions of the Wheeler‐DeWitt equation corresponding to the spacetimes scriptN and scriptB, gives the probability of nucleating the state scriptN relative to the probability of having the state scriptB. 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.

Quantifying the potential and flux landscapes for nonequilibrium multiverse, a new scenario for time arrow

“…In previous studies [7,18,22], the tunneling transition rates from Minkowski and AdS universes to dS universes are assumed to be zero. Recent studies show that there is a possibility of the tunneling transition from Minkowski or AdS vacuum to dS universes through the bounce [8][9][10][11][12][13][14][15]. In [15], the authors showed that if we choose suitable boundary conditions, the detailed balance can be broken down.…”

“…S 1,2,3,4 are certain small constants. Noted that although equation (219) appears to be a numerical setting, it contains the main point that the tunneling may occur from Minkowski (or AdS) universes to dS universes which can break down the detail balance [15] under proper boundary conditions. This feature is captured in the currernt work.…”

“…Recent studies suggested the possibilities of bounces avoiding singularities from a contracting universe (with negative cosmological constant) back to the expanding universe (with positive cosmological constant) [8]. Furthermore, there were also discussions on the possibility of expanding universe (with positive cosmological constant) born from the flat universe (with zero cosmological constant) [9][10][11][12][13][14][15]. If one takes this into consideration, the terminal vacuum (with zero or negative cosmological constant) will have small chances of coming back to the normal vacuum (with positive cosmological constant).…”

“…If one takes this into consideration, the terminal vacuum (with zero or negative cosmological constant) will have small chances of coming back to the normal vacuum (with positive cosmological constant). The detailed balance can be broken in this case [8,14,15]. This suggests a need to study the multiverse problem from a nonequilibrium perspective.…”

Harmonic hybrid inflation

“…In presence of the Z 2 -symmetry breaking our setup contains a whole set of nondegenerate local minima with vacuum energy splitting of order V 0 δ 2 whose vacuum energy increases with increasing φ 1 -distance from the set of global minima at (φ 1 = 0, φ 2 = 2πn/c). Between the local minima of this mini-landscape there will be tunnelling instanton transitions described by Coleman and de Luccia (CdL) [57] (for very recent work re-analyzing CdL tunnelling using the Hamiltonian-Wheeler-DeWitt approach, see [58]).…”