1. Multiverse from a particle physicist’s perspective Taizan Watari (Univ. of Tokyo) KEK PH07 Mar.03 2007 review + ph/0608121 th/0506235 (w/ B. Feldstein and L. Hall )

2. Why is the CC unnaturally small? The CC may take different values in different parts of the “universe.” ---- multiverse The CC may take different values in different parts of the “universe.” ---- multiverse Quantum process of creation of space-time determines weight factor which is sharply peaked at Quantum process of creation of space-time determines weight factor which is sharply peaked at But in nature, But in nature, Baum ’83, Hawking ‘84

3. Why is the CC small but non-zero? The CC may take different values in different parts of the “universe.” ---- multiverse The CC may take different values in different parts of the “universe.” ---- multiverse Only in vacua with small enough CC, galaxies are formed. Only in vacua with small enough CC, galaxies are formed. Weinberg ‘87

4. Density perturbations grow during matter dominance, but not during radiation, curvature or CC dominance. Density perturbations grow during matter dominance, but not during radiation, curvature or CC dominance. As Gravitational bound systems are formed only when As Gravitational bound systems are formed only when Larger CC is more natural, but too large CC is not observed anyway. Larger CC is more natural, but too large CC is not observed anyway. The most natural observed value of the CC The most natural observed value of the CC (roughly) explains the small but non-zero value of the CC in this universe. (roughly) explains the small but non-zero value of the CC in this universe.

5. Plan of the talk Introduction: the CC problem. Introduction: the CC problem. Theoretical framework Theoretical framework Bottom-up approach Bottom-up approach Living on the edge Living on the edge Ex.1: Scanning inflaton potential Ex.1: Scanning inflaton potential Ex.2: Scanning Higgs potential Ex.2: Scanning Higgs potential Big remaining issues Big remaining issues Summary Summary

6. theoretical framework

7. Variety of vacua (theories) Landscape of vacua Parameters: maybe field vev at potential minimum Parameters: maybe field vev at potential minimum e.g. strong CP phase in Peccei-Quinn mechanism e.g. strong CP phase in Peccei-Quinn mechanism Fundamental theory may have multiple vacua Fundamental theory may have multiple vacua motivated by the CC problem motivated by the CC problem Superstring theory so far Superstring theory so far admits enormous number admits enormous number of vacua. of vacua.

8. Probability Distribution Landscape of vacua, density of states Cosmological evolution of multiverse Environmental selection factor poorly known topics of hot debate (for more than 20 years) often difficult to quantify In principle, and follow from theory. Vilenkin ‘95

9. bottom-up approach

10. Living on the Edge Typical values of observables do not depend on the detailed assumptions of tends to be on the edge of the window; majority do not live in the heaven, though not in the hell. The edge of the window can be studied only with the standard model. Environmental selection (usually) depends only on low-energy physics.

11. Ex.1: Scanning inflaton potential fine tuning problem (eta problem) to achieve in slow-roll inflation fine tuning problem (eta problem) to achieve in slow-roll inflation scanning inflaton potential in a multiverse: Potential may be flat enough by chance, somewhere in the multiverse. scanning inflaton potential in a multiverse: Potential may be flat enough by chance, somewhere in the multiverse. Freivogel, Kleban, Martinez, Susskind ‘05

12. Direct transition to a Standard-Model vacuum results in an open universe: no str. formation. Direct transition to a Standard-Model vacuum results in an open universe: no str. formation. Majority of observers live in vacua associated w/ inflaton potentials barely flat enough to allow galaxy formation. Majority of observers live in vacua associated w/ inflaton potentials barely flat enough to allow galaxy formation. Our universe does not have to be flat at 3000 Mpc scale. is expected to be a little smaller than 1 (a slightly open universe). Our universe does not have to be flat at 3000 Mpc scale. is expected to be a little smaller than 1 (a slightly open universe). large inflaton massflat inflaton potential

13. Ex.2: Scanning Higgs Potential the cosmological constant The Higgs VEV sets the weak scale. andare important parameters of nuclear and astrophysics. The other independent combination, or does not seem to be an “anthropic” parameter. Agrawal Barr Donoghue Seckel ‘97, Graesser Salem ‘06

14. 1-Loop Renormalized Potential

15. Vacuum Decay Negative quartic coupling up-side-down potential vacuum tunneling. Vacuum tunneling rate Sher; Casas Espinosa Quiros; Ishidori Ridolfi Strumia

16. Living on the Edge of Vacuum Stability [time t] x [volume of the past light cone (ct)^3] This environmental selection factor does not require much knowledge in astronomy or nuclear physics. If the a priori distribution is weighted toward smaller (negative) value, typical observers do live on the edge of the vacuum meta-stability.

17. Higgs Boson Mass Prediction [ The last term comes from higher orders in the threshold corrections etc.] The environmental selection provides a very hard cut-off. for Feldstein Hall TW ‘06

18. big remaining issues

19. Cosmological Weight and Inflation # of observers the volume of universe?? # of observers the volume of universe?? The weight factor depends exponentially on inflaton parameters. The weight factor depends exponentially on inflaton parameters. Eternal inflation---inflation goes on forever. Eternal inflation---inflation goes on forever. How to compare How to compare infinite volumes infinite volumes two volumes that are two volumes that are causally disconnected causally disconnected inflaton massflat potential What is ?? Runaway problem. Feldstein Hall TW ’05 Garriga Vilenkin ‘05 Linde Garcia-Bellido Garriga Vilenkin Guth...

20. Multi-parameter Scanning I The CC upper bound The CC upper bound What if either or is scanned?? What if either or is scanned?? Too large or too tightly packed galaxies. Too large or too tightly packed galaxies. What if all of are scanned simultaneously?? What if all of are scanned simultaneously?? Graeser Hsu Jenkins Wise ‘04 Tegmark Rees ‘97 Tegmark Aguirre Rees Wilczek ‘05 very complicated to perform a full analysis

21. Multi-parameter scanning II An anthropic solution to the hierarchy problem using nuclear physics (Agrawal et.al. ‘97 ) is actually a constraint on. An anthropic solution to the hierarchy problem using nuclear physics (Agrawal et.al. ‘97 ) is actually a constraint on. What if is scanned, while is kept fixed?? What if is scanned, while is kept fixed?? Is the limit on still there when all the low- energy parameters are scanned?? Is the limit on still there when all the low- energy parameters are scanned?? Graesser Salem ‘06 Astrophysics and nuclear physics are VERY complicated.

22. the CC Problem a flat inflaton potential density perturbations dark matter abundance baryon asymmetry weak / Planck hierarchy Weinberg angle Higgs boson mass q, l Yukawa couplings SymmetryStatistics + Selection Fundamental Theory Cosmological Evolution Universe Multiverse o stable WIMP o lepton Yukawa o SUSY etc. o SUSY GUT o D-term potential o flavor symmetry o Weinberg ’87 o flat spacious univ. o Tegmark-Rees ’97 o str. formation o str. formation (all compatible??) o sensitive o vacuum stability [ not a winner-take-all game ]

23. Higgs Boson Mass Prediction II: Here, an instantaneous reheating after inflation is assumed. If not, the highest temperature of thermal plasma after inflation is higher than the reheating temperature, the analysis and prediction are slightly different.

24. Top Quark Mass Prediction