a solved problem and future perspectives in babychild

a solved problem and future perspectives in baby/child universe formation Stefano Ansoldi University of Udine, Italy with Takahiro Tanaka, Eduardo Guendelman

vacuum decay

vacuum decay tunneling

vacuum decay tunneling in presence of gravity

contents • introduction with some motivations • (some) technical background • approximations • junction conditions (spherical shells, Lorentzian) • junction conditions (spherical shells, Euclidean) • unsuppressed child universes • tunneling • recent work on the tunneling problem • summary and outlook

introduction and motivations Conceptual problem: quantum theory of non-linear fields including gravity

no gr av ity vacuum decay

w ith gr av it y vacuum decay + gravity Contrary to naïve expectation, these are not always negligible, and may sometimes be of critical importance, especially in the late stages of the decay process

introduction and motivations

contents • introduction with some motivations • (some) technical background • approximations • junction conditions (spherical shells, Lorentzian) • junction conditions (spherical shells, Euclidean) • unsuppressed child universes • tunneling • recent work on the tunneling problem • summary and outlook

approximations spherical symmetry we substantially reduce the number of degrees of freedom at least semi-analytical models become possible useful to test conceptual issues in some cases it can also be a natural physical assumption

approximations thin wall approximation

approximations thin wall approximation it allows us to use Israel junction conditions

WKB approximation •

contents • introduction with some motivations • (some) technical background • approximations • junction conditions (spherical shells, Lorentzian) • junction conditions (spherical shells, Euclidean) • unsuppressed child universes • tunneling • recent work on the tunneling problem • summary and outlook

spherical shells (Lorentzian) •

spherical shells (Lorentzian) effective Dynamics A solution of the junction conditions also determines the two signs. A solution of a classical equation for a particle in a potential V(R), plus two expressions for the two signs.

spherical shells (Lorentzian) form of the effective potential

spherical shells (Lorentzian) The only remaining equation in spherical symmetry can be obtained as a first integral of the Euler-Lagrange equation coming from an effective Lagrangian

junction conditions (Lorentzian) Some general results

junction conditions (Lorentzian) Some general results 5.

junction conditions (Lorentzian) Some general results 6.

spherical shells (Lorentzian) •

spherical shells (Lorentzian) • First case: only unbounded trajectories Second case: both bounded and unbounded trajectories. 33

spherical shells (Lorentzian) • First case: only unbounded trajectories Second case: both bounded and unbounded trajectories. 34

spherical shells (Lorentzian) de Sitter, bounded trajectory

spherical shells (Lorentzian) Let us first consider a bounded trajectory in de Sitter spacetime

spherical shells (Lorentzian) Schwarzschild, bounded trajectory

spherical shells (Lorentzian) Let us now consider the bounded trajectory in Schwarzschild spacetime

spherical shells (Lorentzian) The full spacetime is obtained joining the two “colored” domains across the, which is a part of their boundary. This is the global spacetime diagram corresponding to the bounded trajectory: a domain of the de Sitter spacetime is joined across the shell to a domain of Schwarzschild spacetime.

contents • introduction with some motivations • (some) technical background • approximations • junction conditions (spherical shells, Lorentzian) • junction conditions (spherical shells, Euclidean) • unsuppressed child universes • tunneling • recent work on the tunneling problem • summary and outlook

spherical shells (Euclidean)

spherical shells (Euclidean) effective Dynamics A solution of the junction conditions also determines the two signs. A solution of a classical equation for a particle in a potential V(R), plus two expressions for the two signs.

spherical shells (Euclidean) Nevertheless, the momentum (on a classical solution of the equation of motions) can be continued to the Euclidean sector. It is possible to perform the Euclidean junction to have an additional cross-check that the obtained expression could be correct.

junction conditions (Euclidean) Some general results 6. 7.

contents • introduction with some motivations • (some) technical background • approximations • junction conditions (spherical shells, Lorentzian) • junction conditions (spherical shells, Euclidean) • unsuppressed child universes • tunneling • recent work on the tunneling problem • summary and outlook

unsuppressed child universes there are configurations that may allow “unsuppressed” child universe production what does “unsuppressed” mean? we expect an enhanced probability for the process under some appropriate conditions (work in progress)

unsuppressed child universes a very simplified example (purely classical… nothing fancy) “unsuppressed” creation of a child universe out of “almost empty space” the model sphere of strings separating Minkowski and Schwarzschild spacetimes

unsuppressed child universes In our model we will make the following choices: m(R) → matter on the shell such that p= – ρ/2 our shell is a “sphere of strings”

unsuppressed child universes

unsuppressed child universes if there are enough strings c>2/G baby universe is formed independently from the value of the Schwarzschild mass M. Baby universes can thus be produced out of almost empty space Many (classical generalizations can be obtained)

unsuppressed child universes many (classical generalizations can be obtained) cosmological constant inside if the cosmological constant is big enough, creation out of almost empty space is achieved

unsuppressed child universes many (classical generalizations can be obtained) constant surface tension on the bubble if the surface tension is big enough, creation out of almost empty space is achieved

unsuppressed child universes Many (classical generalizations can be obtained) global magnetic monopole “inside” If the bubble energy density content is big enough, creation out of almost empty space is achieved

unsuppressed child universes

unsuppressed child universes child universe production out of almost empty space can be realized quite generically more realistic models: 1. no past singularity 2. suitable matter-energy content they may require not only transplanchian parameters but also quantum tunneling probability enhanced in these scenarios!

unsuppressed child universes some consequences/applications • child universes with transplanchian parameters (excited child universes) are produce more likely and associated with smaller mass black holes (lower action? ) • effective regulators for ultraviolet divergences in quantum gravity? • alternative approach to cosmological constant problem? • unitarity problem and information loss ? • observable signatures of this process ?

contents • introduction with some motivations • (some) technical background • approximations • junction conditions (spherical shells, Lorentzian) • junction conditions (spherical shells, Euclidean) • unsuppressed child universes • tunneling • recent work on the tunneling problem • summary and outlook

tunnelling (the other junctions)

spacetime before the tunneling

spacetime after the tunneling

tunnelling (spacetime/instanton)

tunneling (Euclidean junction) de Sitter, Euclidean trajectory

tunneling (Euclidean junction) Schwarzschild, Euclidean trajectory

tunneling a problem with tunneling B is nothing but the classical action At the WKB level the exponent B is related to the volume of the region of spacetime associated to the tunneling process.

tunneling a problem with tunneling B is nothing but the classical action Approach 1. Use the path-integral approach to estimate B : calculate the volume of the instanton

tunneling a problem with tunneling B is nothing but the classical action Approach 2. use the effective canonical formalism to estimate B : calculate the classical action by integrating the effective Euclidean momentum

tunneling a problem with tunneling B is nothing but the classical action IN SOME CASES APPROACH 1 ← different result → APPROACH 2

tunneling a problem with tunneling IN SOME CASES APPROACH 1 ← different result → APPROACH 2 the cases in which one of the signs changes along the tunneling trajectory… typical examples: creation of false vacuum bubbles (upward tunneling) tunneling with black-hole/wormhole formation

tunneling a problem with tunneling difficulty can be seen in the effective momentum too

contents • introduction with some motivations • (some) technical background • approximations • junction conditions (spherical shells, Lorentzian) • junction conditions (spherical shells, Euclidean) • unsuppressed child universes • tunneling • recent work on the tunneling problem • summary and outlook

This problem is “apparent”! Apparent /əˈpar(ə)nt/: 1. clearly visible or understood; obvious. 2. seeming real or true, but not necessarily so. From an ADAPTED coordinate system to GENERAL SLICING W. Fischler, D. Morgan, J. Polchinski, Phys. Rev. D 42 (1990) 4042 P. Kraus, F. Wilczek, Nucl. Phys. B 433 (1995) 403 w/ T. Tanaka, J. Exp. Theor. Phys. 120 (2015) 460

spacetime during tunneling

spacetime during the tunneling

technical details WARNING notation may be changing!!!

technical details Example Notation

technical details Notation: action, S → I Example

technical details Example Notation

technical details

contents • introduction with some motivations • (some) technical background • approximations • junction conditions (spherical shells, Lorentzian) • junction conditions (spherical shells, Euclidean) • unsuppressed child universes • tunneling • recent work on the tunneling problem • summary and outlook

summary tunneling of a vacuum bubble seemed to be affected by an inconsistency problem (path-integral vs canonical) inconsistency is apparent at WKB level in the thinwall limit (take advantage of arbitrary slicing) HOWEVER not possible to consistently choose the ‘flow’ of Euclidean time at the boundary, and avoid the lapse function to vanish somewhere the above situation appears in upward tunneling and tunneling with black-holes/wormholes processes

work in progress removed one obstacle to upward tunneling and tunneling with black-hole/wormhole formation refined analysis in progress: • what is the effect of the lapse behavior (for example, quantum field propagation on this background)? • can we consistently construct the wave function? • is there any problem with mode functions, boundary conditions, etc. ? • is it possible to perform consistently analytic continuation between Lorentzian/Euclidean regimes?

work in progress a framework that we are considering, O(4) the ‘downward’ process is well studied and understood: we can consider in this context essential features unsuppressed child universe production classical creation from almost empty space seems ok: what happens if we consider tunneling? Schwinger effect in 1+1 de Sitter space the ‘upward’ process is possible: can we make a connection with baby/child universes (tunneling in presence of wormholes/black-holes) Thank you!

tunnelling (the other junctions) de Sitter, unbounded trajectory

tunnelling (the other junctions) Let us now consider the unbounded trajectory

tunnelling (the other junctions) Schwarzschild, unbounded trajectory

tunnelling (the other junctions) Let us conclude with the unbounded trajectory in Schwarzschild spacetime

tunnelling (the other junctions) Again the full spacetime is obtained joining the two “colored” domains. This gives the full spacetime corresponding to the junction along the unbounded shell trajectory.

details From an ADAPTED coordinate system to GENERAL SLICING [We follow P. Kraus and F. Wilczek, Nucl. Phys. B 433, 403 (1995) but see also W. Fishler, D. Morgan and J. Polchinski, Phys. Rev. D 41 (1990) 2638] After solving some constraints, the action can be written as Crucial point: we can integrate And rewrite the action as …

details … It is now possible to rewrite and substitute in the above