MultiverseMultiversefrom a particle physicist’s from a particle physicist’s

perspectiveperspective

Taizan Watari (Univ. of Tokyo)Taizan Watari (Univ. of Tokyo)

KEK PH07 Mar.03 2007KEK PH07 Mar.03 2007

review + ph/0608121 th/0506235 (w/ B. Feldstein and L. Hall )

Why is the CC Why is the CC unnaturally small?unnaturally small?

The CC may take different values in The CC may take different values in different parts of the “universe.” ---- different parts of the “universe.” ---- multiversemultiverse

Quantum process of creation of space-Quantum process of creation of space-time determines weight factor time determines weight factor which is sharply peaked at which is sharply peaked at

But in nature, But in nature,

10 ,e LL :

0.L ;

0.L ¹

Baum ’83, Hawking ‘84

Why is the CC small Why is the CC small but but non-zeronon-zero??

The CC may take different values in The CC may take different values in different parts of the “universe.” ---- different parts of the “universe.” ---- multiversemultiverse

Only in vacua with small enough CC, Only in vacua with small enough CC, galaxies are formed. galaxies are formed.

Weinberg ‘87

Density perturbations grow during Density perturbations grow during matter dominance, but not during matter dominance, but not during radiation, curvature or CC dominance.radiation, curvature or CC dominance.

As As Gravitational bound systems are Gravitational bound systems are formed only whenformed only when

Larger CC is more natural, but too large Larger CC is more natural, but too large CC is not observed anyway. CC is not observed anyway.

The most natural observed value of the The most natural observed value of the CCCC

(roughly) (roughly) explains explains the small but non-zero value of the CC in the small but non-zero value of the CC in this universe.this universe.

(1),Od® 3; ; .DM eq DM eqr r d®

3;[ ].CC DM eqr r d£

3;[ ]CC DM eqr r d»

Plan of the talkPlan of the talk

Introduction: the CC problem.Introduction: the CC problem. Theoretical frameworkTheoretical framework Bottom-up approachBottom-up approach

Living on the edgeLiving on the edge Ex.1: Scanning inflaton potentialEx.1: Scanning inflaton potential Ex.2: Scanning Higgs potentialEx.2: Scanning Higgs potential

Big remaining issuesBig remaining issues SummarySummary

theoretical theoretical frameworkframework

Variety of vacua Variety of vacua (theories) Landscape of (theories) Landscape of

vacuavacua Parameters: maybe field vev at potential Parameters: maybe field vev at potential

minimumminimum e.g. strong CP phase in Peccei-Quinn mechanism e.g. strong CP phase in Peccei-Quinn mechanism

Fundamental theory may have multiple vacuaFundamental theory may have multiple vacua motivated by the CC problemmotivated by the CC problem

Superstring theory so far Superstring theory so far

admits enormous number admits enormous number

of vacua.of vacua.

Probability DistributionProbability Distribution

Landscape of vacua, density of states

Cosmological evolution of multiverse

Environmental selection factor

( ) .i iP x dx

( ) ( ) .i i iA x P x dx

poorly known

topics of hot debate (for more than 20 years)

often difficult to quantify

In principle, and follow from theory. ix ij i jx xs d d=

Vilenkin ‘95

bottom-up bottom-up approachapproach

Living on the EdgeLiving on the Edge

Typical values of observables do not depend on the detailed assumptions of ( ) .i iP x dx

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.

ix

Ex.1: Scanning inflaton Ex.1: Scanning inflaton potentialpotential

fine tuning problem (eta fine tuning problem (eta problem) to achieve problem) to achieve in slow-roll inflation in slow-roll inflation

scanning inflaton potential in a scanning inflaton potential in a multiverse: Potential may be multiverse: Potential may be flat enough by chance, somewhere in flat enough by chance, somewhere in the multiverse.the multiverse.

1( )60O60Hdt

e eò :

Freivogel, Kleban, Martinez, Susskind ‘05

Direct transitionDirect transition to a Standard-Model to a Standard-Model vacuum results in an open universe: vacuum results in an open universe: no no str. formation.str. formation.

Majority of observers live in vacua Majority of observers live in vacua associated w/ inflaton potentials barely associated w/ inflaton potentials barely flat enough to allow galaxy formation.flat enough to allow galaxy formation.

Our universe does not have to be flat at Our universe does not have to be flat at 3000 Mpc scale. is expected 3000 Mpc scale. is expected to be a little smaller than 1 (a slightly to be a little smaller than 1 (a slightly open universe).open universe).

M LW +W

large inflaton massflat inflaton potential

Ex.2: Scanning Higgs Ex.2: Scanning Higgs PotentialPotential

24 2 4( ) .

2 4V H H H

m l=L - +

4 :L the cosmological constant

2 2 / :v m l= The Higgs VEV sets the weak scale.

/QCD vL /PM vand are important parameters of nuclear and astrophysics.

The other independent combination, or does not seem to be an “anthropic” parameter.

l 2 22Hm vl=

Agrawal Barr Donoghue Seckel ‘97, Graesser Salem ‘06

1-Loop Renormalized 1-Loop Renormalized PotentialPotential

24 2 4( )

( ) .2 4

HV H H H

m l=L - +

Vacuum DecayVacuum Decay

Negative quartic coupling up-side-down potential

vacuum tunneling.

284 3| ( )|

0[ ] max [ ( )] max[ ].SM

M

M MM M e

pll

-

<L <LG » G =

Vacuum tunneling rate

Sher; Casas Espinosa Quiros; Ishidori Ridolfi Strumia

Living on the Edge Living on the Edge of Vacuum Stabilityof 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.

0 0( )P dl l

40[ ] 1tlG £

Higgs Boson Mass Higgs Boson Mass PredictionPrediction

[ 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

cl | |cp

l

4[ ]te l- G l

big remaining big remaining issuesissues

Cosmological Weight and Cosmological Weight and InflationInflation

# of observers the volume of # of observers the volume of universe??universe?? The weight factor depends exponentially on The weight factor depends exponentially on

inflaton parameters.inflaton parameters.

Eternal inflation---inflation goes on Eternal inflation---inflation goes on forever.forever. How to compare How to compare

infinite volumesinfinite volumes two volumes that are two volumes that are

causally disconnected causally disconnected

µ

inflaton massflat potential

What is ??dRunaway problem.

Feldstein Hall TW ’05Garriga Vilenkin ‘05

Linde Garcia-Bellido Garriga Vilenkin Guth ...

Multi-parameter Multi-parameter Scanning IScanning I

The CC upper boundThe CC upper bound What if either or is scanned??What if either or is scanned??

Too large or too tightly Too large or too tightly packed galaxies.packed galaxies.

What if all of are scanned What if all of are scanned simultaneously??simultaneously??

3;[ ].CC DM eqr r d£

DMs

r d

DMs

r d

Graeser Hsu Jenkins Wise ‘04

Tegmark Rees ‘97

( , , , )DMCC Bs

rr h dTegmark Aguirre Rees Wilczek ‘05

very complicated to perform a full analysis

Multi-parameter Multi-parameter scanning IIscanning II

An anthropic solution to the hierarchy An anthropic solution to the hierarchy problem using nuclear physics (Agrawal problem using nuclear physics (Agrawal et.al. ‘97 ) is actually a constraint on et.al. ‘97 ) is actually a constraint on . . What if is scanned, while is kept What if is scanned, while is kept

fixed?? fixed??

Is the limit on still there when all Is the limit on still there when all the low-energy parameters are the low-energy parameters are scanned??scanned??

QCD

vL

P

vM QCD

vL

Graesser Salem ‘06

QCD

vL

( , , , , , )s QED u d e Fm m m Ga a

Astrophysics and nuclear physics are VERY complicated.

the CC Problemthe CC Problem a flat inflaton potentiala flat inflaton potential density perturbationsdensity perturbations dark matter abundancedark matter abundance baryon asymmetrybaryon asymmetry weak / Planck hierarchyweak / Planck hierarchy Weinberg angleWeinberg angle Higgs boson massHiggs boson mass q, l Yukawa couplingsq, l Yukawa couplings

Symmetry Statistics + Selection Fundamental TheoryCosmological Evolution

Universe

Multiverse

( , , , , ,...)C u d e Fm m m G

o stable WIMPstable WIMPo lepton Yukawalepton Yukawao SUSY etc.SUSY etc.o SUSY GUTSUSY GUT

o D-term D-term potentialpotential

o flavor flavor symmetrysymmetry

o Weinberg ’87Weinberg ’87o flat spacious flat spacious

univ.univ.o Tegmark-Rees Tegmark-Rees

’97’97o str. formationstr. formationo str. formation str. formation

(all (all compatible??)compatible??)

o sensitivesensitive

o sensitivesensitiveo vacuum vacuum

stability stability

[ not a winner-take-all game ]

Higgs Boson Mass Higgs Boson Mass Prediction II: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 predictionare slightly different.

Top Quark Mass Top Quark Mass PredictionPrediction