IPMU
November 2008

Predictions
from theMultiverse
Lawrence Hall
University of California
Berkeley

Where are we?
Particle Physics and Cosmology:
Standard Model with 30 parameters

EnergyMPl

1019

GeV

Why this theory?
Why these numerical values?
..
.

The conventional argument:
Eventually all determined bysymmetries of the unique theory
I’m not so sure!!

v102

ΛQCD

10−1

me

10−3

Teq

10−9

Λ1/4

10−12



Why this theory?
Why these numerical values?

The Anthropic Principleof Old“The Laws of Physics take their form
because they must allow us,
the observer of these laws,to exist.”
This is giving up!

The Cosmological Constant
Weinberg PRL 1987:

Why so small? An anthropic argument:ΛUniverse becomes astructureless, dilute,
inflating gas

ρvirGalaxies, andtherefore observers,
are able to form

Martell, Shapiro, Weinberg
astro-ph/9701099:

A Catastrophic Boundary

Predicted Dark Energy

Need Theory of a Multiverse!

A Preview of Results
Successful Prediction

Level of accuracy

3/4
1/4v = N1 ΛQCD MPl

2

me = N2 α ΛQCD

2

Teq = N3

1/4 5/4
me ΛQCD100

1/2α MPl

1/2me ΛQCD
1/4Λ
= N4
1/2
α MPl

3623πcf
N44 = 7 2 2rad22 fρ K fb

Alsomu , md ; mt , mH ; Q0 , Mgal

Outline
I. Predictions from the Multiverse

II. The Higgs Boson Mass

III. Nuclear Physics and the Weak Scale
IV. Cosmological Coincidences

I. Predictions from The Multiverse
Many universesx2x1
GG G GG
G GGxobs

x

Environmental selectionusParameters of low energy field theory;or important physical quantities, eg TeqdNobs = f˜(x) n(x) d ln x = f (x) d ln x

Catastrophic Boundariesx2



In many situations there arecatastrophic boundaries -physics makes a suddentransition

 This regime change induces
a sudden change in n(x) The crucial assumption:f˜(x) is peaked
towards the boundary
Most observers
near boundaryABx1n(x)
AB
xcxxcxf˜(x)A Comparison
Symmetries
symmetries restrict the parameter space.
Assumptions:symmetries, representations, symmetry breaking

Multiverse
physics of catastrophic boundaries:
eg nuclear stability, formation of galaxies.

x2

Assumptions:a multiverse force towards the boundary
catastrophic nature of boundary

no observers
most universes∇fx1

Fake and Real Predictionsf˜(x)A fake prediction:

xobs



A real prediction:

xf˜(x)∇f

No observers

Most universes

Calculated from the physics
of the catastrophic boundaryAssume ∇ f sufficiently large

xobs

xcx

Nb1

Nx

“Tip of the Cone”

n2

1x2
∇f

∇fxcx
x1
1 prediction, 1 runaway

1 prediction

x2

2

∇f



x1

Tipof theCone

2 predictions

nn predictions

How close to the Boundary?
Define f(x):Power law:dNobs = f (x) d ln xf ∝xpDefine force:

x1/2

xc
1/p
=2x1/2xxc

F=pGives:∇f1/2∂ ln fF = ∇f =∂ ln xF = p:

532

11/2

1/3

1/5xc
x1/2

1.15

1.26

1.41

24816II) The Higgs Mass
Brian Feldstein, LJH,Taizan Watari;
hep-ph/0608121

VmH

Λv

HV (H)

Galaxies

Avoiding a helium
universe: later

A phaseboundaryv

H

The Phase Boundary
Assume: SM up to some large scale ΛSMV (H)Hv

λ0λ(ΛSM ) = λ0ht (ΛSM ) = h0

∇fh0
EW phase boundary is catastrophic boundary

Environmental
predictions for
mt , mH

Higgs and Top Mass Predictions!
"#"#$
mt − 172.6 GeV
αs − 0.1176− 2.6± 6 GeV
mH = 110.5 + 4.4
1.4 GeV
0.002
2 looprunning

3 loop:Top and QCD
contributions to running→ 109 Arkani-Hamed, Dobovsk

25 GeV+prunning topole

Senatore,Villadoro 0808.2399!
"mt = 176.7 + 2.2 log10$

ΛSM±3GeV1018 GeV

relatively
insensitive toSM cutoff

Suppose LHC finds
only a SM Higgs#p sufficiently large for a tightHiggs mass predictionmH ∼ (120 − 130) GeVmH ∼ 115 GeV

35 GeV− √pp ∼ 1−2p ∼ 10!
!!

III) Nuclear Boundaries
Stability of Nuclei

BBN

Nuclear Stability Boundaries
0.1

0.01

Relevant parameters
0.001
0.001

2d slice

0.01!

me mu md
α,,,mp m
0.1
1 p mpmu/mu,o"

10100

1000

1000

Yasunori Nomura,
LJH
arXiv:0712.2454

100

0.1

0.01

0.001
0.001

65

Tip of theCone!

BD < 0mu,d,estars exotic32no stars

Closeness ton boundary
0.1

4

determined by nuclear
physics of boundaries

mn < m p + me

0.01

md/md,omd/md,o∇f07

mn − m p − me > 8 MeV

118

no complex nuclei
1020Damour
DonoghuearXiv:0712.2968

me = me,o31mu/mu,o

10

1001000(10 - 30)%100

Understanding Coincidences

Why are the threecontributions to Q(n → peν)
comparable?

Q
Q ! 0.8 MeV0me , mu , md
are determined by thephysics of the boundary

Simple distributions give

0.5 MeV

1.0 ∓ 0.5 MeVmeδd−u 2.3 ± 0.5 MeV

δEMFigure 11: Q value for the reaction n → pe− ν̄.

e!
EM(0.5 – 2) are strong interaction coefficie
where CI≈ (0.5 – 2) mandCαδ≈a definition of the QCD scale such that ΛQCD = 100 MeV. Throughout
B [20]. For complex nuclei the binding enranges for mu,o and md,o from Ref.
mu,d ! , BD
Ebin = CB ΛQCD , with CB ≈ 0.08Nanother strong interaction coefficient. The nnuclei boundaries are then described by the inequalities

The BBN BoundaryRelevant quantities:

mn − m p ∝ ΛQCD

1.3 MeVT f (v)

0.8 MeV

YH , YHeYHeYH

Our universe is withina factor 2 of a changeof regime

He universe:
no H burning starsv
1/4
3/4(mn − m p ) MPl

The Weak Scalevvc

Heuniverseheavy nuclei
unstable

runaway direction
window width is factor 2 to 3,
closes up as yu increases

n unstableydc

Our universe is within a factor of 2 ofthe critical pointyd

3/4
1/4vc ∼ ΛQCD MPlydc ∼Does this require a strong force on v?
ie does it exclude dynamical EWSB !?!

!

ΛQCDMPl" 14

The Force on vv

Fv = 2

Heuniverse

Fyd = 0v

Heuniverse

Fyd = 0heavy nuclei
unstable

heavy nuclei
unstable
n unstablen unstable

ydv

Fv = 0

Heuniverse

Fv = 0Fyd = −1heavy nuclei
unstablen unstable

Another BBN boundary:v

Heuniverse

Fv = 0Fyd = 0heavy nuclei
unstableyd
Perhaps preferredydn unstable

HeuniverseydSplit Supersymmetry
Arkani-Hamed, Dimopoulos
th/0405159

mg̃ , τg̃m2

mhh̃u,d couplings

Works even if
Yukawas scan:
3/4
1/4v ! ΛQCD MPlv

Compelling evidence for an
amount of fine tuning of2m15e.g.
102v

Coincidence

Heuniversem2q̃,l,H
˜ u ,Hd , µB

heavy nuclei
unstablen unstableydµ, Mav

˜ H, H + , Aq̃, l,g̃, w̃, b̃, h̃u , h̃d ,hImplication:
Certain crucial parameters are being
related by environmental selectionme ! δEMBmu,d ! , BDN!

yd ∼ΛQCDMPl" 14

3/4
1/4v ∼ ΛQCD MPl

These parameters are not determinedby symmetries or by accidents

At thefactor of 2 levelIV) Cosmological Coincidences
Raphael Bousso,Yasunori Nomura, LJH

 Well separated cosmic eras:
 Broken down recently:

tin f l ! tEW SB ! tQCD ! teqtΛ ! tvir ! trad ! tComp
Amount ofInverse Compton
Amount of
Dark Matter &eg, QED
scattering from CMB
Dark Energy
Size of primordial
bremsstrahlung
density perturbations

Why are these time scales all 109−10years?

Hard to imagine a symmetry explanation
 Seek order of magnitude understanding!!

The Cosmological ConstantΛCatastrophic boundary:must form non-linear protogalaxies before CC fuels inflation

Weinberg PRL 1987ρvir

CC problem solved
Amount of Dark Energy predictedΛ ∼ ρviri.e.

∇ftΛ ∼ tvir

 nobs ∼ nvir B nobs ∼ Scausal diamond

0.8

0.7
1210

9

107

10Bousso, Harnik
Kribs,Perez
hep-th/0702115

0.6

0.6

0.5
Probability density

Probability density

Martell, Shapiro,
Weinberg
astro-ph/9701099

Most universes adilute inflatinghomogeneous gas

0.4

0.4
0.3
0.2

0.20.10.0!124!123!122!121log( !" )!120!119Λ

0.0!126!125!124!123!122log( !" )!121!120!119ΛThe CC Runaway Problem
Suppose ρvir scansΛ∇fρvirf (ρvir , Λ) might reach a maximum at some point

This preserves Λ ∼ ρvir but the value cannot be predicted
Need a second catastrophic boundary

The Galaxy Cooling CatastropheM

Compute ionization andcooling boundaries

Bremsstrahlung rate
too lowMc

Relevant parameters∇fno ionization

α, me , m p ; ρvir , MPl , Mρvircρvirρvirc predicted from proto-galaxy cooling physics:
m4e m2p−34ρvirc ∼ 4 2 ∼ (8 × 10 eV)
α MPl

explaining the coincidence

and as a bonus:Mc ∼4α5 MPl6710∼
10GeV∼
10M"
5/21/2me m ptrad ∼ tvir

Solving the CC Runaway Problem

2 scanning parametersand2 catastrophic boundaries

Λcooling

virialization

Λc

∇fρvirc

m4e m2p−34
Λc ∼ 4 2 ∼ (2 × 10 eV)
α MPl

ρvirInverse Compton Cooling Why is our galaxy so close toinverse Compton cooling?

MBremsstrahlungrate too low

McAll M cool via
inverse Compton

no ionization



ρvirc

Assume Compton
cooling is catastrophic

This radically changes the scanning analysis



Small region in ρvir is tip of higher dimensional cone!
ρvir ∼ Q30 Teq4

(Q0 , Teq )ρvirScanning Q0, Teq
Teq
ρvir ∼ Q30 Teq4∇f

(Q0 , Teq )Teq,cBremsstrahlungrate too low

All M cool via
inverse Compton



mild force totip of cone

Q0c

Q0tComp ∼ trad

Explains the coincidenceTwo predictions

Q0 , Teq are each factor 100 from the critical point; e.g.

meQ0c ∼mp

1/4 5/4
me m pTeq,c ∼1/2
α MPlf (Q0 , Teq ) ∼ Q0 /Teq1/2

Symmetries & The Multiverse
Standard ModelEnvironmental selection does not carewhat the underlying theory isSM

Beyond Standard Model

BSM

Independent parameters that allow for the variation ofme , mu , md , v, Λ, Qo , Teq(Lose Higgs prediction)

Conclusions: A Complete SchemeThe idea:
assume multiverse force
towards catastrophic edges

x2∇fTip of theCone



x1



Nuclear stability

memumd,,ΛQCD ΛQCD ΛQCDvBBN

VirializationΛProto-galaxy cooling:

Teq , Q0

ΛQCD
What determines MPl ?

ΛQCD, ye,u,dMgal

 A missing boundary?
 Multiverse distribution?
 The discretuum?

Will LHC discover unnatural EWSB?