Phase Transitions in the Early Universe

QM2008, Jaipur, Feb. 5th, 2008John Ellis

^

and Late

The CMB according to WMAP

Image of Universe at recombination(atom formation, not itself a phase transition)

Lumpiness due to earlier transition

300,000years

3minutes

1 micro-second

1 pico-second

Recombination:Birth of atoms

Nucleosynthesis:Birth of nuclei

Quark-hadronphase

transition

Electroweak phase transition:

Birth of matter?Inflation?

Birth of Stucture?

Hot and Dense Hadronic MatterCollide heavy nuclei at high energies to create …

… and probe the quark-hadronphase transition

Recreate the first 10-6 seconds …Properties described by

string theory ideas:

viscosity, jet quenching, …?

AdS/CFT Approach to QGP

• Gauge theories in 4 dimensions related to (suitably chosen) gravity/string theory in 5 dimensions:

g: = 5 A

• Rigorous for N= 4 supersymmetry(scale-invariant conformal field theory)

• Heuristic for realistic QCD• Interest because

strong gauge coupling weak string coupling• Reliable calculations for strongly-coupled QGP?

Early Heuristic Discussion

Black Holes in 5 Dimensions

• Consider 5-dimensional AdS space, radius b, metric:

4 Newton constant

• Black holes stable if temperature

T > T1 = 1/b

• Outer horizon of BH = r+

• Consider two limits: b << r+, b >> r+ JE, A.Ghosh, Mavromatos

Black Hole Equation of State

• High-temperature limit b << r+

• Partition function

• Effective potential

• van der Waals equation of state

• Suggestive of phase transition

• Approximate density, pressure

JE, A.Ghosh, Mavromatos

Combined Picture of Transition

• Reminiscent of lattice results

• New insight into underlying dynamics?

• Calculational tool for QGP?

JE, A.Ghosh, Mavromatos

AdS/CFT for N = 4 SUSY Gauge Theory

• N = 4 SUSY QCD has fixed coupling • Rigorous AdS/CFT correspondence at

large (∞, 1/ corrections), large Nc

• Can be used to calculate Wilson loops• Related to static and dynamic quantities• Promising comparison with knowledge of

QCD for T ~ 1.2 to 2.5 Tc

• Challenge to extend to realistic QCD

Viscosity in N = 4 SUSY Gauge Theory

• Potentially interesting for cosmological QCD transition: not yet explored

Very small at large coupling

Lower thanother fluids!

Kovtun, Son, Starinets

Comparison with Lattice Calculations

• N = 4 result similar to lattice for T ~ 2 Tc

• But trace anomaly ≠ 0 QCD not conformal

Electroweak Phase Transition

• Second order in the Standard Model for mH > 114.4 GeV

• Strong first order needed for baryogenesis at the electroweak scale

• Not enough CP violation anyway in the Standard Model

• Both problems may be solved by SUSY

Generating the matter in the Universe

• Need difference between matter, antimatter

C, CP violation seen in laboratory• Need matter-creating interactions

present in unified theories – not yet seen• Need breakdown of thermal equilibrium

possible in very early Universe

e.g., in first-order phase transition

Sakharov

Could a first-order electroweak transition be the culprit?

Electroweak Transition in SUSY

• First order electroweak phase transition if additional light scalar

• Most plausible candidate: light stop• Beware of development

of stop v.e.v.• Parameter space very

tightly constrained• Higgs and/or stop

close to discoveryQuiros

Baryogenesis in SUSY

• Additional sources of CP violation

• ‘Easy’ to get sufficient baryon/entropy

• Favours relatively

light CP-odd Higgs

• Modest CP-violating

phase is enough

Quiros

Implications of SUSY Baryogenesis

• mH < 120 GeV, 120 GeV < mstop < mt

• 5 < tan < 10, small stop mixing

• CP-violating phase ~ 0.1

• Important limits from electric dipole moments

Balazs, Carena, Menon, Morrissey, Wagner

Implications for SUSY Dark MatterParameter region changeswith CP violating phase

Scattering may be reduced

as CP-violating phase

Balazs, Carena, Menon, Morrissey, Wagner

Low-Energy Effects of CP Phases

Bs

b s

Bu

Different

regions

allowed for

different

phases … … and hence

ACP in

b sJ.E. + Lee + Pilaftsis: arXiv:0708.2078

Cosmological Inflation

• Theory to explain the size, age & uniformity of the Universe

• Period of (near) exponential expansion driven by scalar field energy (1)

• Quantum effects → CMB anisotropies, origins of structures

• Subsequent reheating → matter (2)• Then matter-antimatter asymmetry generated

Origin of Structures in Universe

Small quantum fluctuations: one part in 105

Gravitational instability: Matter falls into

the overdense regions

Convert into matter with varying density

The CMB according to WMAP

Image of Universe at recombination(atom formation, not itself a phase transition)

Lumpiness due to earlier transition

• Upper limit on Hubble expansion rate during inflation

Higgs Mass and Inflation

• Upper limit on reheating temperature from metastability

Espinosa, Giudice, Riotto

A Phase Transition in the Future?

• Our electroweak vacuum may be unstable if mH small (hinted by electroweak data)– Renormalization by top quark drives Higgs

self-coupling < 0 at large <H>

• Metastable vacuum, lifetime = f(mH, mt, s)– mH too small would have decayed– mH too large will ‘never’ decay– mH, mt, s just right: Big Bang Big Crunch

On our Way to a Big Crunch?

Renormalization by top quark coupling

New vacuumwith 0|H|0 >

mH =125120115105GeV

Big Crunch!Arkani-Hamed, Dubovsky, Salvatore, Villadoro

Is there a Big Crunch in Our Future?

Present errors

Big Crunch for mH = 114.4 GeV

Future errors

Eternal expansion

Big Crunch!Big Crunch allowed @ 1.5

Arkani-Hamed, Dubovsky, Salvatore, Villadoro

Outlook

• Phase transitions in early universe might have been very important:– Origin of structures– Origin of matter– Size of Universe, …(and there may be another in the future)

• Quark-hadron transition only one directly accessible to experiment

• Go to it!