Paul StankusOak Ridge

RHIC/AGS Users’ Meeting June 20, 05

Hitchiker’s Guide: QGP in the Early Universe

Paul StankusOak Ridge Nat’l Lab

APS 06 April Meeting

Contents Big Bang Basic Framework �

Nuclear Particles in the Early �Universe; Limiting Temperature?

Thermal Quarks and Gluons; �Experimental Evidence

If I can understand it, so can you!

Henrietta Leavitt American

Distances via variable stars

Edwin Hubble American

Galaxies outside Milky Way

The original Hubble Diagram“A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae” E.Hubble (1929)

USUS USUS

Now

Slightly Earlier

As seen from our position: As seen from another position:

Recessional velocity distance

Same pattern seen by all observers!

Original Hubble diagram

Freedman, et al. Astrophys. J. 553, 47 (2001)

1929: H0 ~500 km/sec/Mpc

2001: H0 = 727 km/sec/Mpc

Photons

t

x

UsGalaxies

?

vRecession = H0 d

1/H0 ~ 1010 year ~ Age of the Universe?

1/H

0

W. Freedman Canadian

Modern Hubble constant (2001)

H.P. Robertson American

A.G. Walker British

W. de Sitter Dutch

Albert Einstein German

A. Friedmann Russian

G. LeMaitre Belgian

Formalized most general form of isotropic and homogeneous universe in GR “Robertson-Walker metric” (1935-6)

General Theory of Relativity (1915); Static, closed universe (1917)

Vacuum-energy-filled universes “de Sitter space” (1917)

Evolution of homogeneous, non-static (expanding) universes “Friedmann models” (1922, 1927)

€

dτ 2 = −ds2 = dt 2 − a(t)[ ]2dχ 2

a(t) dimensionless; set a(now) =1

χ has units of length

a(t)Δχ = physical separation at time t

Robertson-Walker Metric€

dτ 2 = −ds2 = dt 2 − dx 2

H. Minkowski German

“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (1907)

Minkowski Metric

t

t1

t2

Photons

Us Galaxies at rest in the “Hubble flow”

t

t=now

€

χ = constant

"At rest in the Hubble flow"

Galaxies

€

dτ = 0 ⇒dt

dχ= ±a(t)

Photons€

H(t) =velocity

distance=

d

dta(t)Δχ[ ]

a(t)Δχ=

˙ a (t)

a(t)

Hubble Constant

A photon’s period grows a(t)

Its coordinate wavelength is constant; its physical wavelength a(t) grows a(t)

(t2)/(t1) = a(t2)/a(t1) 1+z

Cosmological Red Shift

Robertson-Walker Coordinates

w=P/

-1/3

+1/3

-1

a(t)eHt

a(t)t1/2

a(t)t2/3t

now

acc

dec

Inflation, dominated by

“inflaton field” vacuum energy

Radiation-dominated thermal equilibrium

Matter-dominated, non-uniformities grow (structure)

Acceleration in a(t), domination by cosmological constant and/or vacuum energy.

a(t) depends on pressure/energy: The New Standard Cosmology in Four Easy Steps

€

dE = TdS − PdVBasic

Thermodynamics

Sudden expansion, fluid fills empty space without loss of energy.

dE = 0 PdV > 0 therefore dS > 0

Gradual expansion (equilibrium maintained), fluid loses energy through PdV work.

dE = -PdV therefore dS = 0Isentropic Adiabatic

Hot

Hot

Hot

Hot

Cool

Golden Rule 1: Entropy per co-moving volume is conserved

Golden Rule 3: All chemical potentials are negligible

Golden Rule 2: All entropy is in relativistic species

Expansion covers many decades in T, so typically either T>>m (relativistic) or T<<m (frozen out)

€

Entropy S in co - moving volume Δχ( )3preserved

Relativistic gas S

V≡ s = sParticle Type

Particle Type

∑ =2π 2

45

⎛

⎝ ⎜

⎞

⎠ ⎟T 3

Particle Type

∑ =2π 2

45

⎛

⎝ ⎜

⎞

⎠ ⎟g∗S T 3

g∗S ≡ effective number of (Boson) relativistic species

Entropy density S

V=

S

Δχ( )3

1

a3=

2π 2

45g∗S T 3

€

T ∝ g∗S( )− 1

31

aGolden Rule 4:

g*S1 Billion oK 1 Trillion oK

Start with light particles, no strong nuclear force

g*S1 Billion oK 1 Trillion oK

Previous Plot

Now add hadrons = feel strong nuclear force

g*S1 Billion oK 1 Trillion oK

Previous Plots

Keep adding more hadrons….

How many hadrons?

Density of hadron mass states dN/dM increases exponentially with mass.

Prior to the 1970’s this was explained in several ways theoretically

Statistical Bootstrap Hadrons made of hadrons made of hadrons…

Regge Trajectories Stretchy rotators, first string theory

€

dN

dM~ exp M

TH

⎛ ⎝ ⎜ ⎞

⎠ ⎟

Broniowski, et.al. 2004TH ~ 21012 oK

Rolf Hagedorn GermanHadron bootstrap model and limiting temperature (1965)

€

E ~ E i gi

states i

∑ exp −E i /T( ) ~ EdN

dE∫ exp −E /T( ) dE

€

E ~ MdN

dM∫ exp −M /T( ) dM now add in

dN

dM~ exp M /TH( )

~ M∫ exp −M1

T−

1

TH

⎡

⎣ ⎢

⎤

⎦ ⎥

⎛

⎝ ⎜

⎞

⎠ ⎟ dM

Ordinary statistical mechanics:

For thermal hadron gas (crudely set Ei=Mi):

Energy diverges as T --> TH

Maximum achievable temperature?

“…a veil, obscuring our view of the very beginning.” Steven Weinberg, The First Three Minutes (1977)

Karsch, Redlich, Tawfik, Eur.Phys.J.C29:549-556,2003

/T4

g*S

D. GrossH.D. PolitzerF. Wilczek

American

QCD Asymptotic Freedom (1973)

“In 1972 the early universe seemed hopelessly opaque…conditions of ultrahigh temperatures…produce a theoretically intractable mess. But asymptotic freedom renders ultrahigh temperatures friendly…” Frank Wilczek, Nobel Lecture (RMP 05)

QCD to the rescue!

Replace Hadrons (messy and numerous)

by Quarks and Gluons (simple

and few)

Ha

dro

n g

as

Thermal QCD ”QGP” (Lattice)

Kolb & Turner, “The Early Universe”

QC

D T

rans

ition

e+e- A

nnih

ilatio

n

Nuc

leos

ynth

esis

D

ecou

plin

g

Mes

ons

free

ze o

ut

Hea

vy q

uark

s an

d bo

sons

free

ze o

ut

“Before [QCD] we could not go back further than 200,000 years after the Big Bang. Today…since QCD simplifies at high energy, we can extrapolate to very early times when nucleons melted…to form a quark-gluon plasma.” David Gross, Nobel Lecture (RMP 05)

Thermal QCD -- i.e. quarks and

gluons -- makes the very early universe tractable; but where is the experimental

proof?

g*S

National Research Council Report (2003)

Eleven Science Questions for the New

Century

Question 8 is:

Also: BNL-AGS, CERN-SPS, CERN-LHC

BNL-RHIC Facility

Low High

Low High

Density, PressurePressure Gradient

Initial (10-24 sec) Thermalized Medium Early

Later

Fast

Slow

€

v2 =px

2 − py2

px2 + py

2

Elliptic momentum anisotropy

PHENIX Data

Fluid dynamics predicts momentum anisotropy correctly for 99% of particles

produced in Au+Au

• Strong self-re-interaction

• Early thermalization (10-24 sec)

• Low dissipation (viscosity)

• Equation of state P/ similar to relativistic gas

What does it mean?

Beam energy

• High acceleration requires high P/ pressure/energy density. Hagedorn picture would be softer since massive hadrons are non-relativistic.

• Increase/saturate with higher energy densities. In Hagedorn picture pressure decreases with density.

Momentum anisotropy increases as we increase beam energy & energy density

What does it mean?

Thermal photon radiation from

quarks and gluons?

Ti> 500 MeV

Direct photons from nuclear collisions suggest initial temperatures > TH

1. B violation2. C,CP violation

3. Out of equilibrium

Sakharov criteria for baryogenesis

Most of the early universe is QCD!

Dissipation could be relevant here:

Mean Free Path ~ de Broglie

€

η Shear viscosity

s Entropy density< ~ 0.1

Quantum Limit! “Perfect Fluid”

Ideal gas Ideal fluidLong mfp Short mfp

High dissipation Low dissipation

Data imply (D. Teaney, D. Molnar):

Conclusions•The early universe is straightforward to describe, given simplifying assumptions of isotropy, homogeneity, and thermal equilibrium.

•Strong interaction/hadron physics made it hard to understand T > 100 MeV ~ 1012 K.

•Transition to thermal QCD makes high temperatures tractable theoretically; but we are only now delivering on a 30-year-old promise to test it experimentally.

References

Freedman & Turner, “Measuring and understanding the universe”, Rev Mod Phys 75, 1433 (2003)

Kolb & Turner, The Early Universe, Westview (1990)

Dodelson, Modern Cosmology, Academic Press (2003)

Weinberg, Gravitation and Cosmology, Wiley (1972)

Weinberg, The First Three Minutes, Basic (1977, 1993)

Schutz, A First Course in General Relativity, Cambridge (1985)

Misner, Thorne, Wheeler, Gravitation, W.H.Freeman (1973)

Backup material

Side-to-beam view

Along-the-beam view

Hot Zone

Au+Au at √sNN = 200 GeV

STAR Experiment at RHIC

€

dτ 2 = −ds2 = dt( )2 − dx( )

2 − dy( )2 − dz( )

2

= d ′ t ( )2 − d ′ x ( )

2 − d ′ y ( )2 − d ′ z ( )

2

€

dx 0 ≡ dt dx1 ≡ dx dx 2 ≡ dy dx 3 ≡ dz

dτ 2 = −ds2 = gμν dx μ dxν

gμν =

1 0 0 0

0 −1 0 0

0 0 −1 0

0 0 0 −1

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

Metric

Tensor

Complete coordinate freedom! All physics is in g(x0,x1,x2,x3)

H. Minkowski German

“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (1907)

x

t

t’

x’

Photons

Photons

E1

E1

E2

E2

E0

E0

B. Riemann German

Formalized non-Euclidean geometry (1854)

a(t) a Friedmann-Robertson-Walker (FRW) cosmology

Three basic solutions for a(t):

1. Relativistic gas, “radiation dominated”

P/ = 1/3 a-4 a(t)t1/2

2. Non-relativistic gas, “matter dominated”

P/ = 0 a-3 a(t)t2/3

3. “Cosmological-constant-dominated” or “vacuum-energy-dominated”

P/ = -1 constant a(t)eHt “de Sitter space”

€

T00 = ρ Energy density (in local rest frame)

€

˙ a

a

⎛

⎝ ⎜

⎞

⎠ ⎟2

= H 2 =8π

3Gρ −

1

r02a2

Curvature

€

Critical ≡3H 2

8πGρ

ρ Cr≡ Ω Ω =1⇒ Flat

Q: How does change during expansion?

Friedmann Equation 1 (=0 version)

€

˙ ̇ a

a= −

4πG

3ρ + 3P( )

Friedmann Equation 2 (Isen/Iso-tropic fluid,=0)

However, this cannot describe a static, non-empty FRW Universe.

Ac/De-celeration of the Universe’s expansion

€

If ρ (t) ≥ 0 and P(t) ≥ 0 then

˙ a (t) ≥ 0 and ˙ ̇ a (t) ≤ 0, and then

a(t) = 0 for some t

Necessity of a Big Bang!

Over-

€

Something

about space- time

curvature

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

=

Something

about

mass- energy

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

€

Metric Tensor gμν

Riemann Tensor Rαβγδ

Ricci Tensor Rμν = Rαμαν

Ricci Scalar R = Rαα

€

Stress- Energy Tensor Tμν

€

Rμν −1

2Rgμν

For continuity

≡ Gμν Einstein Tensor

1 2 4 4 3 4 4 − Λ

Unknown{ gμν = 8πGNewton

To match Newton

1 2 4 3 4 Tμν

€

Gμν = 8πTμν Einstein Field Equation(s)

B. Riemann GermanFormalized non-Euclidean geometry (1854)

G. Ricci-Curbastro Italian Tensor calculus (1888)

€

˙ ̇ a

a= −

4πG

3ρ + 3P( )

€

˙ a

a

⎛

⎝ ⎜

⎞

⎠ ⎟2

= H 2 =8π

3Gρ −

1

r02a2

With freedom to choose r02 and , we can arrange

to have a’=a’’=0 universe with finite matter density

Einstein 1917 “Einstein Closed, Static Universe”

disregarded after Hubble expansion discovered

- but -

“vacuum energy” acts just like

Friedmann 1 and 2:

€

Gμν − Λgμν = 8π Tμν rearrange Gμν = 8π Tμν + Λgμν

Gμν = 8π

ρ M +Λ

8π0 0 0

0 PM −Λ

8π0 0

0 0 PM −Λ

8π0

0 0 0 PM −Λ

8π

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

≡ 8πT Effμν

Re-introduce “cosmological constant”

Generalize (t)=Matter(t) +/8 P(t)=PMatter(t)

-/8

Cosmological constant acts like constant energy density, constant negative pressure, with EOS P/ = -1

T(t)

a(t)(t)

t

How do we relate T to a,? i.e. thermodynamics

The QCD quark-hadron transition is typically ignored by cosmologists as uninteresting

Weinberg (1972): Considers Hagedorn-style limiting-temperature model, leads to a(t)t2/3|lnt|1/2; but concludes “…the present contents…depends only on the entropy per baryon…. In order to learn something about the behavior of the universe before the temperature dropped below 1012oK we need to look for fossils [relics]….”

Kolb & Turner (1990): “While we will not discuss the quark/hadron transition, the details and the nature (1st order, 2nd order, etc.) of this transition are of some cosmological interest, as local inhomogeneities in the baryon number density could possible affect…primordial nucleosythesis…”

Weinberg, Gravitation and Cosmology,

Wiley 1972

Golden Rule 5: Equilibrium is boring!Would you like to live in thermal equilibrium at 2.75oK?

Example of e+e- annihilation transferring entropy to photons, after neutrinos have already decoupled (relics).