Vacuum decay and the end of the universe. Ian Moss Newcastle University January 2014

Transcription

1 Vacuum decay and the end of the universe Ian Moss Newcastle University January 2014

2 Outline metastable vacuum decay in curved space seeded nucleation* late universe *Ruth Gregory, Ian Moss, Ben Withers, arxiv:

3 Metastable-vacuum decay V Coleman: vacuum decay can FV TV be described by an instanton φ(r 2 +τ 2 ) representing the nucleation of a bubble of the true vacuum. τ t FV FV Callan,Coleman, Phys Rev D

4 Nucleation rate The bubble nucleation rate is determined by the Euclidean action, =Ae B B = I b I v In the thin wall approximation B =2 2 R R 4 Energy density ε Tension = (2V ) 1/2 d Bubble radius R c =3 /

5 Thermal bubbles τ FV B =4 R R 3 B changes by a factor R C /T - but ε changes

6 In curved space The decay time can be larger than the Hubble time and then we get inflation. In an expanding universe, both first and second order phase transitions can supercool. old inflation (Guth) new inflation (Linde,Albrecht,Steinhart)

7 CDL instanton Compexify the time in the scalar field and the metric: Coleman De Luccia instanton. False vacuum 4-sphere CDL instanton B CDL = ( l 2 ) 2 l =(8 G 2 /16 ) 1/2 Coleman, De Luccia Phys Rev D

8 Lorentzian picture time radius

9 Thick wall limit Can have a weakly first order phase transition by reducing the barrier height

10 Seeded nucleation Most supercooled phase transitions are nucleated by impurities and imperfections. Hiscock, Phys Rev D ; Gregory, Moss, Withers

11 Black hole seeds true vacuum black hole remnant seed Hiscock, Phys Rev D ; Gregory, Moss, Withers

12 Suppose bubbles nucleate in the false vacuum on de Sitter space-time with a black hole of mass M and de Sitter radius l 2 =3/(8 G ) In static coordinates where ds 2 = f(r)dt 2 + dr2 f(r) + r2 d 2 f(r) =1 2GM r r 2 l 2 In the thin wall limit the wall is at R(t)

13 Lorenzian spacetime rh rc R(t) Static patch or causal diamond

14 Integrate the Einstein equations to get R(t) Ṙ(t) 2 + U(R) =0 0.5 U R Γ Parameters: M S, M R, ε, Static case M S

15 The instanton is obtained by sending t to -iτ r min r max ( ) r h r c r( ) As usual, assume =Ae B B = I b I v This gives the correct result for the CDL case. In the static case, action is independent of the conical deficit. A WKB argument backs up the result.

16 General case There is a critical seed mass M C = ( l 2 ) 2 M S <M C : no remnant M S >M C : remnant with mass M R l =(8 G 2 /16 ) 1/2

17 The nucleation rate in enhanced compared to the CDL case M S <M C B B CDL s{= M + êm N GM N = l/ 27

18 M S >M C 1.5 B 1.0 B CDL M + êm N

19 WKB approach Ṙ(t) 2 + U(R) =0 {P 2 + U(R)} =0 Tunnelling probability is given by the same instanton. Conjecture that there is a crossing symmetry. Farhi,Guth,Guven, Nucl Phys B , Fischler,Morgan,Polchinski Phys Rev D

20 Evaporation vs nucleation For the static bubble with no remnant, the nucleation exponent is B*=4πG M 2. The nucleation pre-factor A contains (B/2π) for each zero mode and determinant 1/(GM*): = 2/G e 4 GM 2 Hawking evaporation rates are roughly H = (G 2 M 3 ) 1 Γ H Γ* for masses around the Planck mass.

21 Correcting for Hawking evaporation The potential is modified*: V(φ) M =V(φ) 0 + yφ tt M Calculate on a black hole background. *IGM Phys Rev D

22 The late universe We may live in a metastable vacuum. Phase transitions can be triggered by thermal processes-but nature provides limits Size matters: high temperatures can stabilise the vacuum. Shape matters: spherical shapes are optimal for transitions. Cosmic rays: 4000 FeFe TeV collisions per cubic parsec per second*. *Hut, Rees, Nature , Buzra et al Rev Mod Phys

23 Safe regions 100 unexplored region 10 1 size (fm) neutron stars RHIC LHC cosmic rays U H E(GeV)/V

24 Outlook What is the theory of vacuum decay in curved space-time (beyond just an analogy)? Do singular instantons play a role? How stable is the string landscape? Can black holes seed nucleation in low Planck mass scenarios?