Jonathan Pearson- Formation and Evolution of Kinky Vortons

8/3/2019 Jonathan Pearson- Formation and Evolution of Kinky Vortons

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Formation and Evolution of

Kinky VortonsJonathan Pearson

Jodrell Bank Centre for Astrophysics,

University of Manchester, U.K.

UK Cosmology Conference, Kings College London, Nov 2009


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Outline

Kinky vortons review model & properties

Numerical implementation

Results & interpretation

Domain wall networks & their scalingdynamics usually scale out as t-1

Elastic dark energy & condensed matterphysics


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Quick review of domain walls

Degenerate vacuaField chooses which to occupy

Spatial clumps in same minima = domain

Transition region = domain wall

V()

- +

+

-

x


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The model

U(1)symmetry term

Domain forming term Interaction term

Kinetic terms

Global U(1) x Z2symmetrySymmetry broken in Z2vacuum

U(1) symmetry retained

U(1) symmetry has conserved Noether charge


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Kinky vortons

Solutions toequations of

motion

kink solution

condensate Construct ring solutions

k = N/R

Nwinding number

Stable kink solution with charged condensate

- stable radii computed for given N& charge Q

- charge flows along kink

Kinky Vortons,

Battye & Sutcliffe, 2008


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Numerical evolution

Solve equations of motion via leapfrog evolver

Discretise space to fourth order

Discretise time to second order

Periodic boundary conditions

- sets max time simulation valid

(signal interferes with itself

via toroidal boundary)

Initial conditions:

random domains (zero velocity)

homogeneous charge

Number gridpoints

(2+1)


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Evolution of number of walls

Increase initialcharge density

normalscaling

solution

Increasing initial charge

slows wall evolution

Number almost freezes

to constant value


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Videos of evolution

Evolve from P = 10242,with Q = 0.09

Q

Red/blue: positive/negative

Grey: less than 10% maximum value

Black lines: domain walls

100 time-steps per second (50fps)


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Re()

Slow-motion

(25fps)

Watch blue/red

flow along wall

Grey: less than 40%

maximum value


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Images of

(colours = each domain, P = 4096)

Time

80 160 320 640 1280

Zero charge: Z2discrete model

Domain walls scale out as fast as possible


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Images of

Time

Initial

charge

density

(colours = each domain, P = 4096)

0

0.01

0.09

0.25

80 160 320 640 1280

Q(0)


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Run Past t =

1x 2x 3x 4x

Time (multiple of)(colours = each domain, P = 1024)

0.09

0.25


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Configurations Re()

Red/blue = positive/negative

Grey = 10% threshold from max

Q(0) = 0.09 at

t = 640

Winding along

domain wall(instances of red/blue)


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Configurations Q,|J|2

Q |J|2

Charge andcurrent find the walls, condensing on them


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Properties of loops

To check that loops are kinky vortons, must checkN-Q-Rrelationship holds: compute R* from measured N,Q

- only approximation, as highly non-circular- do for loops from Q(0) = 0.09

1

2

3


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Conclusions

Loops long-lived & have properties of kinky

vortons

Form from random initial conditions

Charge & current (i.e. winding) prevents wall

collapse via charge conservation

Domain wall network does not scale in

standard way Reinvigorate as dark energy model!


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Formation and Evolution of

Kinky VortonsJonathan Pearson

Jodrell Bank Centre for Astrophysics,

University of Manchester, U.K.

UK Cosmology Conference, Kings College London, Nov 2009

Talk based upon JCAP09(2009)039

arXiv:hep-th/0908.1865

(written with R.Battye, P.Sutcliffe & S.Pike)

Documents

Jonathan Pearson- Formation and Evolution of Kinky Vortons