The Best of Worlds, the Worst of Worlds...

THE BEST OF WORLDS, THE WORST OF WORLDS...

Alejandro Jenkins

High Energy Physics, FSU

[email protected]

LNS Nuclear & Particle Physics Colloquium,

MIT

8 Nov. 2010

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HISTORY OF THIS UNIVERSE

Source: NASA, WMAP science team

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COSMIC MICROWAVE BACKGROUND (CMB)

Electromagnetic radiation, made 377,000 years after initial singularity, when protons combined with electrons to make neutral hydrogen

Predicted by Gamow in ‘46, actively searched for by Dicke et al. in the 60’s

Accidentally discovered by Penzias & Wilson in ’64 [Nobel Prize ’78]

First precision measurements in ’89 by COBE (NASA) [Nobel Prize ’06 to Smoot & Mather]

2001 WMAP (NASA); 2007 Planck (ESA)

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Source: NASA

COSMOLOGICAL QUANDARIES

Flatness problem: Why is the geometry of the universe so close to being Euclidean?

Horizon problem: Why is the universe so homogeneous?

Monopole problem: Why aren’t magnetic monopoles abundant?

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Illustration from D. Castelvecchi, “The Growth of Inflation,” Symmetry, Dec. 2004 / Jan. 2005. Notebook on display at Chicago planetarium

Brief period of exponential expansion, sometime between 10-36 and 10-32 s after initial singularity

From a billionth of the size of a proton, to maybe the size of an orange

Increase in volume by at least 1078

Proposed by Alan Guth to address the flatness, horizon, and monopole problems

Predicted the correct (scale-invariant) spectrum for primordial density pertubations, as reflected in the CMB

P�(k) � k�3

INFLATION

INFLATIONARY MULTIVERSE

Illustration from Andrei Linde, Sci. Am., Nov. 1994

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EXTRA DIMENSIONS

From Bousso & Polchinski, Sci. Am. Sep. 2004

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STRING LANDSCAPE

Bousso & Polchinski, op. cit.

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FUNDAMENTAL VS. ENVIRONMENTAL

Inflation & string theory seem to describe something more than observable Universe

Quantities we think of as fundamental could instead be environmental

Analogies: sizes of planetary orbits, speed of sound, etc.

Kepler, Mysterium Cosmographicum (1596)

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COPERNICAN PRINCIPLE

Human life doesn’t have privileged position in the universe, or in the scheme of physics

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Andreas Cellarius, Harmonia Macrocosmica (1661)

ANTHROPIC PRINCIPLE

Observed conditions have to be compatible with the existence of conscious, intelligent life, and this is a non-trivial restriction

from ESA website

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WORD OF CAUTION

The anthropic principle was named by Brandon Carter (’74) but use in modern science dates back at least to Boltzmann in 1877

It’s always been controversial

Steven Weinberg: “A physicist talking about the anthropic principle runs the same risk as a cleric talking about pornography: no matter how much you say you are against it, some people will think you are a little too interested.”

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BEST OF WORLDS?

Various arguments about physics being fine-tuned for life, such as:

3-α synthesis of carbon in stars (Hoyle, ’64)

proton-neutron mass difference

cosmological constant

John D. Barrow and Frank J. Tipler, The Anthropic Cosmological Principle,(Oxford U. Press, New York, 1986), 706 P.

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WORST OF WORLDS?A teleologist [...] praises the wise arrangement which provides that planets do not collide, that land and sea are kept apart, that all is not petrified by cold nor roasted by heat, that the Earth’s axis is inclined so that there is no eternal spring and fruit might ripen, etc., etc.

Arthur Schopenhauer (1788-1860)

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But these and all similar things are simply necessary conditions. If there is to be a world at all, if its planets are to exist at least long enough for a ray of light from a remote fixed star to reach them [...] then, of course, it cannot be framed so unskillfully that the very scaffolding threatened to collapse [...]

Against the palpably sophistical proofs of Leibniz that this is the best of all possible worlds, we may even oppose seriously and honestly the argument that it is the worst of all possible worlds.

– Schopenhauer, The World as Will and Idea, vol. III, ch. 46, (1818)

WORST OF WORLDS? (BIS)

Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design,(Little, Brown and Co., New York, 2005), 416 P.

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MAYBE NEITHER?

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AJ & Gilad Perez, Sci. Am., Jan. 2010

UNITS

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c = 1

� = 1

[length] = [time] = [energy]�1 = [mass]�1

me = 0.5 MeV

MPl = (8�G)�1/2 = 2� 1018 GeV

COSMOLOGICAL CONSTANT

Λ is like a constant energy density of otherwise empty space-time

Λ>0 causes space-time to stretch exponentially (inflation)

Λ<0 causes space-time to re-collapse (“Big Crunch”)

Current rate of expansion of the universe consistent with Λ>0

Unnaturally small, by 123 orders of magnitude!

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� � 10�123M4Pl

Gµ� = M�2Pl Tµ� � �gµ�

Space-time curvature

Cosmological constant

Matter & energy

COSMOLOGICAL CONSTANT

Weinberg (’87) predicted Λ>0, before it was measured (’98)

This was anthropic, worst-of-worlds reasoning:

Λ as big as can be, while still allowing Universe to develop some structure

No convincing dynamical explanation of smallness of Λ (“dark energy”)

Only minor increase of Λ could be offset by other parameters

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BAYESIAN STATISTICS

AJ & Gilad Perez, op. cit.

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Multiverse theory in trouble if

Anthropic constraint

Multiverse distribution

pmeasured({�i}) � p({�i}|observer)

� p(observer|{�i}) · p({�i})

r � pmeasured{�⇥i }pmeasured{��i }

⇥ 1

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Bayesian statistics with a single data point!

HIGGS MECHANISM

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As  explained  to  William  Waldegrave  (UK  minister  of  science)  by  Prof.  David  J.  Miller,  1993  

Illustrations by CERN, from Prof. Miller’s website

“Vacuum”:

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Massive particle:

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Higgs boson:

HIGGS MECHANISM, CONT.

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�ud

⇥

L

; uR, dR

� =�

⇥+

⇥0

⇥; �c � i�2��

Lflavor = �yuq̄L�cuR � ydq̄L�dR + h.c.

For  each  !lavor,  we  have

Coupled  to  Higgs  doublet

by

Higgs  potential

V (�) = �µ2�†� + ���†�

⇥2

��⇥ =�

0v/⇤

2

⇥gives  vacuum  expectation  value  (VEV)

HIGGS MECHANISM, CONT.

Gives f a Dirac mass:

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v =�

µ2/�

Sheldon Glashow: “toilet of the Standard Model”

μ2, λ, and y’s are free parameters

μ2  subject to large, additive quantum corrections

�µ2 = � |yf |2

8�2⇥2

UV + . . .

Expect μ2 ~ (100 GeV)2, while ΛUV2 ~ (1018 GeV)2

mf =1�2yfv

WEAK SCALE

v also sets range of weak nuclear force

Responsible for radioactive β-decay (interconverts protons and neutrons)

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1range

�Mweak =12gv

Mystery: the weak force isn’t weak enough!

Old Gargamelle bubble chamber, CERN

GAUGE HIERARCHY PROBLEM

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M2weak

M2Pl

� 10�32

Hierarchy seems to require implausible fine-tuning of parameters (as first pointed out by Ken Wilson in the 70’s)

This has motivated 30+ years of theoretical work: supersymmetry, technicolor, little Higgs, large extra dimensions, etc.

All propose new physics, yet unseen, just above Mweak

WEAK SCALE: WORST OF WORLDS?

By analogy to cosmological constant, can this be resolved anthropically?

Agrawal, Barr, Donoghue & Seckel ’98, argued that, if all other parameters of the SM are fixed, stable atoms require:

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Argument based on quark masses, relative to ΛQCD (scale of strong nuclear force)

0 < Mweak � 5M�weak

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Un

In other universes!

From the pages of

THE WEAKNESS WAY OF LIFE

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Harnik, Kribs & Perez, ’06Image: AJ & Perez, op. cit.

WEAKLESS UNIVERSE, CONT.

Harnik, Kribs & Perez, ’06Image: AJ & Perez, op. cit.

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BARYOGENESIS

Why was Universe formed with more matter than antimatter?

Requires breaking charge-parity (CP) symmetry

Weak sector of SM breaks CP (Kobayashi & Maskawa ’73, Nobel Prize ’08) but by far too little to explain observed matter abundance

Whatever explains baryogenesis here could also work in weakless universe

Weakless universes may have heavy relic baryons and leptons

Might cause trouble, or not

Plausible to find some weakless universes without heavy relics

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�⇥b ⇥ 10�2�⇤b�⇤b � 10�10

WHY DO WE SEE A WEAK FORCE?

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In Standard Model, particle masses given by

Gauge hierarchy problem:

Observed masses suggest scale-invariant distribution for yf’s

vacuum expectation value of the Higgs field

Our v2 is ~ 1032 times too small

Yukawa coupling

p(v) � v2

M2pl

for 0 < v < Mpl

p(y) � 1y

Common feature of complex dynamics

(“Benford’s Law”)

QCDΛ

1 GeV 10 GeV100 MeV10 MeV1 MeV0.1 MeV0.01 MeV 100 GeV

u d bs c te μ τ

Mweak

cf. Donoghue, Dutta, Ross & Tegmark, ’09

mf =1�2yfv

HIERARCHY PROBLEM IN MULTIVERSE

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Oram Gedalia, AJ & Gilad Perez, arXiv:1010.2626

M

y

weak

f

10-15

10-12

10-9

10-6

10-3

10-18

MPl

eud

10-21

10-24

FLAVOR PUZZLE

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CSM = det�YuY †

u YdY†d

⇥� 10�22

Summing  over  ;lavors:

“Jarlskog  determinant:”

For  generic,  order-­‐one  complex  matrices,  we’d  have:

CSM � 0.1

Large  hierarchies  of  masses  and  mixings

Not  subject  to  large  quantum  corrections,  but  certainly  not  anthropic!

Lflavor = �(yu)ij q̄iL�cuj

R � (yd)ij q̄iL�dj

R + h.c.

FLAVOR DYNAMICS

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Flavor puzzle should be resolved dynamically

30 years of work on possible models generically gives

y � �Q

ε universal, Q flavor-dependent (cf.  Froggat  &  Nielsen  ’79;  Dimopoulos  &  Susskind  ’79;  Eichten  &  Lane  ’80;  Kaplan  ’91;  Arkani-­‐Hamed  &  Schmaltz  ’99)

For p(Q) � Qn

Far  more  likely  to  live  in  weakless  universe,  unless  n  <  -­‐  21  

If  n  <  -­‐  21,  getting  observed  Yukawas  drives  ε  <<  1  

Could  be  hierarchy  problem  of  its  ownOram Gedalia, AJ & Gilad Perez, arXiv:1010.2626

OUTLOOK

Possible that fundamental theory won’t predict observed world uniquely

Statistics in multiverse & anthropic principle may be relevant to theoretical physics

Our current ideas of the string theory landscape / inflationary multiverse seem too unrestrictive

Our nuclear interactions do not seem typical of congenial universes

Still need better understanding of dynamics of multiverse (or whatever’s out there)

Expect new physics at LHC

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THANK YOU!39

Cornelis Saftleven,(Dutch, circa 1612 - 1681),The College of Animals,oil on canvasDallas Museum of Art