Hi Higgs and the Cosmos d th C Kerson Huang MIT 2013 1 After - PowerPoint PPT Presentation

Hi Higgs and the Cosmos d th C Kerson Huang MIT 2013 1

After decades of search, the Higgs particle was the Higgs particle was discovered at CERN, in a reaction like this In a detector like this In a detector like this Higgs & Englert got the Physics Nobel Prize in 2013, for , postulating the underlying Higgs field, in 1964. 2

The Higgs field fills the vacuum. On microscopic scale , p , it gives mass to elementary particles: W, Z, quarks. On macroscopic scale On macroscopic scale , it flows like a superfluid, due to phase variations. On cosmic scale , it makes the universe a superfluid. p 3

Great puzzles of our time: • Dark energy D k • Dark matter Theme of this talk: • Dark energy = energy of Higgs superfluid gy gy gg p • Dark matter = density variation of superfluid 4

Expanding universe • The more distant the galaxy, the faster it moves away from us. • Fabric of space ‐ time expands, like balloon being blown up. • Extrapolate backwards to “big bang” a Edwin Hubble 1889 ‐ 1953 Hubble’s law: Velocity proportional to distance 1 da 1 H   Hubble’s parameter: Hubble s parameter: H  9 a dt 15 10 yrs

Dark energy – deviation from Hubble’s law Accelerated expansion: Driven by “dark energy” 6

Dark matter Velocity curve of Andromeda (Rubin & Ford, 1970) 7

Collision of two galaxy clusters (the “bullet cluster” 2004) g y ( ) Hot gases (x ‐ rays) Galaxies (visible) Dark ‐ matter halo (from gravitational lensing) 8

Dark energy & dark matter constitute 96% of the energy in the universe. tit t 96% f th i th i 9

Superfluidity Quantum phase coherence over macroscopic distances Order parameter: complex scalar field 10

Liquid helium below critical temperature 2.18 K becomes superfluid. It can climb over walls of containers. 11

Superconductivity = superfluidity arising from electron pairs in a metal p y g p Inside a superconductor there is a Inside a superconductor, there is a condensate of electron pairs with definite quantum phase. Phase difference between two superconductors causes a supercurrent to flow from one to the other to flow from one to the other. J Josephson junction h j ti 12

The Higgs field • is a complex scalar field that permeates all space, • serving as order parameter for superfluidity, • making the entire universe a superfluid • making the entire universe a superfluid. It is a quantum field • with momentum scale set by a cutoff momentum. • It undergoes renormalization under a scale transformation. 13

Renormalization As scale changes, one must adjust couplings so as to preserve the theory. • The system’s appearance changes • The system s appearance changes, • But its identity is preserved. Ignore Cutoff  Cutoff  0 0 Hide Effective cutoff  Momentum spectrum 14

Scalar Field Lagrangian density : High momentum cutoff =   = High momentum cutoff 1          2 L V 1 2 Length scale =   Potential :     V  V                      2 4 6 • Renormalization makes the Renormalization makes the 2 2 4 4 6 6 couplings, and thus V, dependent on the length scale. Equation of motion : q • This dependence is especially Thi d d i i ll      2 important when the scale changes V 0 rapidly, as during the big bang. 15

RG (renormalization group) trajectory • The potential V changes as scale changes. • The Lagrangian traces out a trajectory in the space of all possible Lagrangians. • Fixed points correspond to scale ‐ invariant systems. UV trajectory: Asymptotic freedom IR trajectory: Triviality 16

The Creation    • At the big bang . • There was no interaction. • Universe was at the Gaussian fixed point i h G i fi d i • It emerges along some direction in the space of Lagrangians, on an RG trajectory. • Direction < ‐‐ > form of the potential V. Outgoing trajectory ‐‐‐ Asymptotic freedom Ingoing trajector Ingoing trajectory ‐‐‐ Triviality (free field) Tri ialit (free field) 17

      exp z Halpern ‐ Huang potential the only asymptotically free scalar potential • Kummer function (non ‐ polynomial) • Exponential behavior at large fields 18

Cosmological equations 1    R g R 8 G T ( E instein's equation)    2      2 V 0 ( S calar field equation) R obertson-W alker m etric (spatial hom ogeneity) G ravity scale = (radius of universe) a  S calar field scale = (cutoff m om entum ) S ince there can be only one scale in the universe,   = a a Dynamical feedback: Gravity provides cutoff to scalar field Gravity provides cutoff to scalar field, which generates gravitational field. 19

The big bang Initial ‐ value problem   a Ha k = curvature parameter = 0, +1, ‐ 1   k k a V V       2 H  2 a 3 a Trace anomaly  V         3 H      k 2 1        2 2 Constraint equation   X H V 0   a 3 2  X 0 is a constraint on initial values.   Equations guarantee X 0. 20

? Time The big bang Model starts here O(10 ‐ 43 s) • Initial condition: Vacuum field already present. • Universe could have been created in hot “normal phase”, then make phase transition to “superfluid phase”.

Numerical solution   p H t exp       1 p a p t Dark energy without Dark energy without “fine ‐ tuning” problem 22

Comparison of power ‐ law prediction on galactic redshift with observations ‐‐ > earlier epoch d L = luminosity distance Different exponents p only affects vertical displacement, such as A and B such as A and B. Horizontal line corresponds to Hubble’s law. Deviation indicates accelerated expansion (dark energy). Crossover transition between two different phases B ‐ > A (?) 23

Generalization to complex scalar field Generalization to complex scalar field New physics: • Superfluidity • Quantum turbulence 1. Matter creation: Must create enough matter for subsequent nucleogenesis before Must create enough matter for subsequent nucleogenesis before universe gets too large. 2. Decoupling of matter scale and Planck scale: p g Matter interactions governed by nuclear scale of 1 GeV. But equations have built ‐ in Planck scale of 10 18 GeV. These scales should decouple from each other. 24

Quantized vortex in complex scalar field   Fe i   i  ∇   superfluid velocity  d s  ∇   2  n C 25

A “worm ‐ hole” cosmos • Replace vortex core by tube. • Scalar field remains uniform outside. The vortex ‐ tube system • Can still use RW metric, represent emergent • but space is multiply ‐ connected. degrees of freedom. 26

Vortex dynamics Elementary structure is vortex ring Self ‐ induced vortex motion v  1 R 4  R ln The smaller the radius of curvature R, R 0 the faster it moves normal to R. 27

Vortex reconnection • The cusps spring away from each other at “infinite” speed (due to small radii), d (d ll d ) creating two jets of energy. • Efficient way of converting • Efficient way of converting potential energy to kinetic energy in very short time. 28

Magnetic reconnections in sun’s corona Responsible for solar flares p 29

Simulation of quantum turbulence Creation of vortex tangle in presence of “counterflow” . K W Schwarz Phys Rev B 38 2398 (1988) K.W. Schwarz, Phys. Rev. B 38 , 2398 (1988). Number of reconnections: Number of reconnections: 0 3 18 18 844 844 1128 14781 Fractal dimension = 1.6 D. Kivotides, C.F. Barenghi, and D.C. Samuels. Phys. Rev. Lett. 87 , 155301 (2001).

Cosmology with quantum turbulence • Scalar field has uniform modulus F . • Phase dynamics manifested via vortex tangle l . • Matter created in vortex tangle. Equations of motion q Variables Variables   a a Radius of universe from Einstein's equation with RW metric.            T T = T T T T T T F F M d l Modulus of scalar field f l fi ld Source of gravity: S f i   tot F    Vortex tube density F from field equation.      Matter density Matter density from Vinen's equation. q  T   from = energy-momentum conservation 0.  tot; 31

Vinen’s equation for quantum turbulence q q    vortex tube density (length per unit spatial volume) vortex tube density (length per unit spatial volume)    2 2 3 / 2 3 / 2       A A B B G ro w th D e c a y • Vinen (1957) Vinen (1957) • Schwarz (1988) • Verified by experiments in superfluid helium. 32