Phase Transitions in the Early Universe QM2008, Jaipur, Feb. 5th, 2008 John 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

300,000 years 3 minutes 1 micro- second 1 pico- second Recombination: Birth of atoms Nucleosynthesis: Birth of nuclei Quark-hadron phase transition Electroweak phase transition: Birth of matter? Inflation? Birth of Stucture?

Hot and Dense Hadronic Matter Collide heavy nuclei at high energies to create … … and probe the quark-hadron phase transition Recreate the first 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 > T 1 = 1/  b Outer horizon of BH = r + Consider two limits: 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 N c 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 T c 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 than other fluids! Kovtun, Son, Starinets

Comparison with Lattice Calculations N = 4 result similar to lattice for T ~ 2 T c But trace anomaly ≠ 0  QCD not conformal

Electroweak Phase Transition Second order in the Standard Model for m H > 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 discovery Quiros

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 m H < 120 GeV, 120 GeV < m stop < m t 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 Matter Parameter region changes with CP violating phase Scattering may be reduced as CP-violating phase  Balazs, Carena, Menon, Morrissey, Wagner

Low-Energy Effects of CP Phases B s   b  s  Bu  Bu   Different regions allowed for different phases … … and hence A CP in b  s  J.E. + Lee + Pilaftsis: arXiv:

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 10 5 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 m H small (hinted by electroweak data) –Renormalization by top quark drives Higgs self-coupling Metastable vacuum, lifetime = f(m H, m t,  s ) –m H too small  would have decayed –m H too large  will ‘never’ decay –m H, m t,  s just right: Big Bang  Big Crunch

On our Way to a Big Crunch? Renormalization by top quark coupling New vacuum with  0|H|0  >  m H = GeV Big Crunch! Arkani-Hamed, Dubovsky, Salvatore, Villadoro

Is there a Big Crunch in Our Future? Present errors Big Crunch for m H = GeV Future errors Eternal expansion Big Crunch! Big Crunch 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!