our runaway universe -- the discovery and implication of the 2011 nobel prize in physics

NTU Joint Physics ColloquiumNovember 1, 2011

Department of Physics and Graduate Institute of AstrophysicsNational Taiwan University

&Leung Center for Cosmology and Particle Astrophysics

National Taiwan University

Pisin Chen

1NTU Joint Physics Colloquium, 2011

2011 Nobel Prize for Physics


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Standard Candle

NTU Joint Physics Colloquium, 2011

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Hubble’s great discovery: Universe is expanding

v = H0 a

Using Type I Cepheids as standard candle NTU Joint Physics Colloquium, 2011

General Relativity Equivalence between gravity and curvature

廣義相對論：重力 =幾何曲率

Gμν + Λgμν =8πGc4 Tμν .

愛因思坦方程 (1915):

1918 年愛因思坦引進宇宙常數以確保宇宙穩定

1929 年哈伯發現宇宙膨脹之後 , 愛因恩坦宣稱引進宇宙常數是他一生最愚蠢的錯誤 “The biggest blunder of my life”. 5

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Hubble Expansion - Interpretation

Friedmann-Robertson-Walker (FRW) metric:

ds2 =-dt2 +a(t)2(dr2 + r2dΩ2)

a(t2)a(t1)

a(t): scale factor

Hubble parameter can be expressed as H = a ⁄ a ˙


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Expansion of Universe governed by the Friedmann eqs.,

cosmological constant

H

g

+ H 2 =&&aa=−

4πG3

(ρ + 3p) +Λ3

curvature signature

H 2 =

&aa

⎛⎝⎜

⎞⎠⎟

2

=8πG3

ρ −ka2 +

Λ3

Newton’s constant


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• Critical density: • Total and fractional densities radiation: matter (baryon & cold): cosmology constant: • Friedmann eq. again:

• Equation of state For accel. universe, For cosmological constant, In general, w can depend on a, e.g.,

ρc=3H28πG

H2H02=Ωra4+Ωma3+Ωka2+ΩΛ ρ=wp w=w0+wa1−a() w=−1 Dominant at early times

Dominant at late times


Ωr = ρ r / ρ c

Ωm = ρm / ρ c

Ω =ρtotal / ρ c

ΩΛ =ρΛ / ρ c

w < −1 / 3

Cosmic Acceleration: SN-Ia as Standard Candle1998 Discovery!

Riess et al, 1998 Perlmutter et al, 1999High z Supernova Team Supernova Cosmology Project


Accelerating Expansion (1998): One of the biggest surprises in science!


11For Einstein, even the biggest blunder in his life turns out to be so profound!

“Extraordinary claims requires extraordinary evidence.”

To constrain the nature of dark energy we need to be able to measure the expansion rate of the Universe and there are three main approaches:

• Standard candles: which measure the luminosity distance as a function of redshift.

• Standard rulers: which measure the angular diameter distance and expansion rate as a function of redshift.

• Growth of fluctuations.

NTU Joint Physics Colloquium, 2011 12

Baryon Acoustic Oscillations

NTU Joint Physics Colloquium, 2011 13

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Consistent with all

observations:

ΩΛ = 0.76 ± 0.02


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Evidence for past deceleration: Evidence for past deceleration: Important reality checkImportant reality check

HST ACS Sample of high-z SNe: A. Riess et al, Ap.J 607, 665 (2004)

Rocky Kolb, SSI 2003

?

?

(extra gravity)

(anti-gravity)

73%

23%

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暗能暗質


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What we understandWhat we understand• Smooth, very elastic, non-particulate (medium)

• Extremely weak interaction with ordinary matter

• Insignificant at small scales, important at large scales

• Insignificant at early times, important at late times

• Isotropic and homogeneous (apparently)


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• Vacuum energy/cosmological constant• Destiny of the Universe• Related to Dark Matter, Inflation, Neutrino Mass?• Connections to SUSY/Superstrings/Extra dimensions?• Signal of new gravitational physics?• Hole in the Universe?• Connection to the hierarchy problem?

Dark Energy is a profound mystery because it touches so many other

important puzzles


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Theoretical AttemptsTheoretical Attempts• Assume General Relativity (GR) is correct. Einstein equation:

Introduce (anti-)gravity - simplest model: cosmological constant

Commonly associated with vacuum energy. - dynamical models: rolling scalar field with potential (quintessence, phantom, etc.)

Gμν =8πGTμν −Λgμν

geometry gravity

Einstein tensor energy-momentum tensor

Λ =8π Gρ vac

w < −1 / 3

w =−1

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Theoretical AttemptsTheoretical Attempts• Quintessence - Accelerating expansion caused by the potential energy of a scalar field. - It must be very light (large Compton wavelength) so it won’t clump or form structures.

ρφ =&φ / 2 + V (φ)

pφ = &φ / 2 − V (φ) &&φ+ 3H &φ +

dV

dφ= 0,

H 2 =H02 Ωr (1+ z)4 +Ωm(1+ z)3 +Ωφ 3 [1+wφ(z')]

dz'1+ z'0

z

∫⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥.

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Theoretical AttemptsTheoretical Attempts• Assume General Relativity (GR) is correct. Einstein equation:

Gμν =8πGTμν −Λgμν

geometry gravity

Einstein tensor energy-momentum tensor

Special place in the universe - Anti-Copernican Principle: “We are special”. - No need for .Λ

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Theoretical AttemptsTheoretical Attempts• General Relativity (GR) is the problem - Modify Einstein-Hilbert action

to something more general:

- DGP model string-theory-inspired IR modification of GR - Emergent gravity GR as an effective theory emerging from quantum theory of gravity

SEH =1

8πGd4x −g∫ R

Ricci Scalar

SMG =1

8πGd4∫ x −g R+ f(R)[ ].

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Some Challenges• Cosmological constant: simple and natural. But

what makes it so small?• Quintessence: Who ordered it? Renormalized

scalar field often acquires large mass. • “Anti-Copernican Principle”: hard to modify enough

to accommodate cosmic acceleration and satisfy other constraints (importance of dynamical tests)

• Modified GR: hard to satisfy short-distance constraints while providing significant departure at large distance.


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Observations show that Dark Energy = CC?

p =wρw=w0 +wa(1−a)

2009 data:


w =−1

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The Cosmological Constant ProblemThe Cosmological Constant Problem• Cosmological constant has long been a problem in theoretical physics during most of the 20th century.• Since 1998, it has further become one of the most challenging issues in astrophysics in the new century.• Several excellent review articles: S. Weinberg (1989), Carroll (2000), Sahni & Starobinsky (2000, 2006), Peebles & Ratra (2002), Padmanabhan (2003)… More than 1000 papers in arXiv that has ‘cosmological constant’ in the title. Can’t possibly cover all ideas. NTU Joint Physics Colloquium, 2011

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What is the Problem?What is the Problem?• History After completing his formulation of general relativity (GR), Einstein (1917) introduced a cosmological constant (CC) to his eq. for the universe to be static:

As is well-known, he gave up this term after Hubble’s discovery of cosmic expansion. Unfortunately, not so easy to drop it. In GR, anything that contributes to the energy density of the vacuum acts like a CC.


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The Old CC ProblemThe Old CC ProblemThe old (< 1998): • Lorentz invariance, upon which QFT is based, tells us that in the vacuum the energy-momentum tensor must take the form This is equivalent to adding a term to CC:

• Quantum vacuum (zero point) energies with cutoff at Planck scale gives

⟨Tμν ⟩= −⟨ρ⟩gμν .

Λeff = Λ + 8πG⟨ρ⟩. ρV = ⟨ρ⟩+ Λ / 8πG = Λeff / 8πG.

ρV ~ M Pl4 ~ 10112 eV 4 .


What is Quantum vacuum Energy?

• Heisenberg Uncertainty Principle:

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ΔxΔp ≥h

2πΔtΔE ≥

h

2π

Vacuum is not empty, but filled with fluctuating energies.


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Quantization of Spacetime

Planck scale:

lP =hG2πc3 ≈1.6 ×10−35m

EP =hc2πG

≈1.2 ×1019

[GeV / c2 ]Ultimate vacuum energy:

EP4 : (1019 GeV )4

=10112[eV]4NTU Joint Physics Colloquium, 2011

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• Astrophysics, however, demands that it must be smaller than the critical density of the universe:

This is 124 orders of magnitude in discrepancy!• Evidently QVE should not gravitate. Otherwise our universe would not have survived until now. • This conflict between GR and quantum theory is the essence of the longstanding CC problem, which clearly requires a resolution. In short,

We shall call this the “old” CC problem.

Why doesn’t quantum vacuum energy gravitate?

ρV ≤ ρ cr ~ 10−12 eV 4 .


The New CC Problem, or the The New CC Problem, or the Dark Energy PuzzleDark Energy Puzzle

The new (>1998) • The dramatic discovery of the accelerating expansion of the universe ushers in a new chapter of the CC problem.

• The substance responsible for it is referred to as the dark energy (DE), described by its equation of state

• According to GR, accelerating expansion can happen if . Einstein’s CC corresponds to

p =wρ, p: pressure, ρ: density

w < −1 / 3 w =−1. 33NTU Joint Physics Colloquium, 2011

• DE=CC remains the simplest and most likely answer. • New challenge: after finding a way, hopefully, to

cancel the CC to 124 decimal points, how do we reinstate 1 to the last digit and keep it tiny? That is,

• We shall call this the “new” CC problem, or the DE puzzle.

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Why is CC nonzero but tiny?


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Why much smaller than standard model scale?

Observations

If dark energy never changes in space and time, then it must be associated with the fundamental

properties of spacetime!

Attempt 1: Attempt 1: Casimir Energy in Extra-DimensionsCasimir Energy in Extra-Dimensions

MCC ; ρDE1/4 : 10−3eV

ρDE1/4

M SM

: 10−15 !

PC, Nucl. Phys. Proc. Suppl.173, 137 (2007).PC and J-A. Gu, Mod. Phys. Lett. A22, 1995 (2007); arXiv:0712.2441


20th Century

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3 gauge interactions are at TeV scale; why is gravity so much weaker, at Planck scale?

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A Numerical CoincidenceA Numerical Coincidence

• A remarkable numerical coincidence, a ‘gravity fine structure constant’:

• Perhaps not accidental but implies a deeper connection:

• Caution: Unlike the 1st hierarchy that links 4 fundamental interaction strengths, DE must be a secondary, derived quantity.


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Analogy in Atomic PhysicsAnalogy in Atomic Physics

• Bohr atom• Fundamental

energy scale in Schrödinger equation: me

• Ground state energy suppressed by 2 powers of fine structure constant

• Dark energy• Fundamental

energy scale in quantum gravity: MPl

• Dark energy suppressed by 2 powers of “gravity fine structure constant”NTU Joint Physics Colloquium, 2011

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Randall-Sundrum Model to bridge the Randall-Sundrum Model to bridge the hierarchy between SM and gravity scales hierarchy between SM and gravity scales

M SM

M Pl

=e−πkR ~10−16

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Casmir Energy: Casmir Energy: Evidence of vacuum fluctuations Evidence of vacuum fluctuations

Casimir energy induced by fields in the RS bulk on the TeV brane gives rise to DE as we set out to look for:

This may solve the New CC Problem.It, however, still does not address the Old CC Problem…

- “Gauge Theory of Gravity with de Sitter Symmetry” (PC, MPLA (2009) [arXiv:1002.4275]) 1.In GR Einstein equation is a 2nd order differential eq. and thus the nature of CC is undetermined:

1.If the field eq. is higher (e.g., 3rd) order instead, then the CC term is not allowed. To recover the well tested GR, one should integrate it once. Then CC is recovered through the constant of integration determined by the boundary condition of the universe.

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Attempt 2: Boundary Condition of the Universe


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• Motivations for Gauge theory of gravity (GG) - To reformulate gravity as a gauge theory - To hopefully quantize gravity theory - To substantiate the ‘constant of integration’ approach as a means to solve the CC problem.

C. N. Yang (1983): “In [ ] I proposed that the gravitational equation should be changed to a third order equation. I believe today, even more than 1974, that this is a promising idea, because the third order equation is more natural than the second order one and because quantization of Einstein’s theory leads to difficulties.”


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Here’s how it goesHere’s how it goes• In GG, the gauge potential (affine connection) is the dynamical variable, which determines the curvature tensor • In close analogy with Maxwell theory, the action for gravity reads (Cook 09)

where the “gravitational current” ( = covariant deriv.)

and

Rαβμν =∂μΓ

αβν −∂νΓ

αβμ + Γα

τμΓτβν + Γα

τνΓτβμ .

SG =κ dx4 −g∫ RαβμνRαβμν +16π J μαβΓ

αβμ( ),

J μαβ =

2Gc4 ∇αT

μβ −∇βT

μα⎡

⎣⎤⎦,

Tμβ =T μ

β −12δ μ

βT, T =T μμ .

∇α


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Field EquationsField Equations• Varying against , we arrive at the field eq. This and the Bianchi identity, together determine the curvature tensor. • Now we recall that and that covariant divergence of is identically 0. Therefore the field eq. of GG removes the CC term by construction.• Integrating this eq. once, we recover the Einstein eq. with a constant of integration which is associated with the boundary condition of the universe.

SG Γμαβ

∇νRμναβ = −4π J μ

αβ .

∇λRαβμν +∇ν Rαβλμ +∇μ Rαβνλ = 0,

Γαμν =1

2∂ν gαμ + ∂μ gαν − ∂α gμν⎡⎣ ⎤⎦,

gμν


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de Sitter Universe as Asymptotic de Sitter Universe as Asymptotic Limit of Hubble Expansion Limit of Hubble Expansion

• Now we invoke our second assumption, that the universe is inherently de Sitter, where the 4-spacetime is a hyperboloid of a 5-d Minkowski space with the constraint where is the radius of curvature of dS. • dS universe as asymptotic limit of Hubble expansion. • Observation gives so we find

−x02 + x1

2 + x22 + x3

2 + x42 = ldS

2

ldS

ΩDE = ρ DE / ρ cr ; 0.75,

ldS ; 1.33H0 ~ 1.5 ×1028cm.NTU Joint Physics Colloquium, 2011

But why did our universe choose such a geometry?!

Anthropic Principle: “Our Universe is one that is suitable for

intelligent habitat.”

String theory allows for a “landscape” of universes (10500!)


Redshift

L

um

inos

ity

Dis

tan

ce

(cm

)

1026

1027

1028

1029

0.01 0.1 1 10

New!GRB

CalibratedGRB

GRB data (z < 1.755) GRB data (1.755 < z < 8.2)

＋ Type Ia SNe

(Ωm, ΩΛ) = (1, 0)

(0.3, 0.7)

(0, 1)

z = 8.2z = 8.2

Yonetoku, GRB workshop, Kyoto, 2010

Hubble Diagram ( 1.8 < z < 8.2)


.

Need to have better measurements of GRB prompt signals.

The Future: certain class of GRB maybecome a new standard candle

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UFFOUFFOUltra Fast Flash ObservatoryUltra Fast Flash Observatory

For observation of early For observation of early photons from Gamma Ray photons from Gamma Ray

BurstsBursts

Korea USA Russia Taiwan Denmark Spain Norway France Poland

http://uffo.ewha.ac.kr


At the turn of the 20th century, two “dark clouds” in physics (a la Lord Kelvin): the Michelson-Morley

experiment and the blackbody radiation, had later developed into revolutionary storms of Relativity and

Quantum Mechanics. At the turn of the 21st century, a new dark cloud – the

dark energy, appears above the horizon. Will the history repeat itself and turn this into another revolutionary

storm in physics, a storm that would clean up the conflict between QM and GR?


our runaway universe -- the discovery and implication of the 2011 nobel prize in physics

Documents

department of physics

expansion of universe

standard candles

standard rulers

expansion rate

standard candle1998

cosmology constant

riess et