Cosmological Defect and High Energy Experiments

1
Cosmological Defect andHigh Energy Experiments

• Michiyasu NAGASAWA
• Department of Information Sciences,
• Kanagawa University

nagasawa_at_info.kanagawa-u.ac.jp
March 12, 2007, CTP, Egypt
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Introduction
standard Big-Bang cosmology unification theory
(inflationary cosmology) including
SUSY
phase transition in the early universe
symmetry breaking scale
cosmological defects (topological
non-topological)

• classification by component fields

• classification by
• vacuum structure

• global defects scalar fields
• local (gauged) defects
• scalar fields gauge fields

• domain wall
• string
• monopole
• texture
• complex defects

anti-monopole
monopole
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Defect Contributionto Cosmic Energy Density
density parameter

• domain wall

• monopole

phase transition temperature
monopole mass
monopole problem

• string

1 string of horizon length per horizon
density perturbation
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Cosmic String
phase transition
loop
core radius

string solution
global string
line energy density
gauged string
cutoff scale
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Kibble Mechanism
correlation length
correlation volume
The phase cannot be determined at the boundary.
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Initial String Number Density

• 80 in the energy belongs to the infinite string.
• The rest, 20, forms loops.

• loop number density

loop length
loop radius

• 1 infinite string per horizon volume

total length

• phase transition during inflation
• (The symmetry is restored by the curvature
  correction.)

the largest domain
domain number density of size
MN Yokoyama, 1992
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Frictional Regime
Aulakh, MN Soni, 1998
The temperature when the frictional force
becomes negligible and the string begins to
move freely due to its tension can be estimated
to be
.

• initial formation epoch

• transient regime

,
correlation scale of infinite string
string moving velocity
phase transition time

• friction dominated era

stretching regime
,
Kibble regime
,

• scaling regime

,
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Scaling Distribution of String

• energy density of infinite string

number of string per horizon

• loop number density of size,

radiation dominant

matter dominant

and also depend on .
,
ratio of loop creation size to horizon
local
energy loss rate
global
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Multiple Winding String
winding number
The string configuration with fixed winding
number can be determined essentially by one
parameter, .
scalar mass
self coupling
gauge mass
gauge coupling
The calculation of the string line energy density
shows multi-winding strings are stable for
and unstable for . Moreover, the
inter-vortex force is attractive for and
repulsive for .
When , the topological inflation
occurs at the GUT scale.
,
de Laix, Trodden Vachaspati, 1998
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Electroweak Baryogenesis

• necessary conditions for baryon number generation

• B violation sphaleron transition
• C and CP violation model extension?
• departure from thermal equilibrium
• It can be satisfied by the electroweak
  scale
• string even if the electroweak phase
• transition is not of first order. When
  ,
• sphaleron bound states may be realized
• which suggests a new scenario of
• baryogenesis.

Soni, 1997
Multi-winding strings can be produced
initially or by following evolution.
Okabe MN, 1999
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Stabilization of Embedded Defects
embedded defects (unstable at zero temperature)
finite temperature plasma
early universe
stabilized
asymmetry between charged scalar components and
neutral ones
destabilization because of
temperature decrease
core phase transition, decay
superconducting ?
In various unification models, more kinds of
cosmological defects can be produced than it has
been expected.
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Embedded String
Although the configuration of embedded
defects satisfies equations of motion, they are
topologically, and in general also dynamically
unstable.
ex.) three real scalar fields
no string
freezing out certain components
string !
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Electroweak String
baryogenesis?
one example of embedded gauged string

• standard model of electromagnetic and weak
• unification

electroweak phase transition
ex.) infinitely long straight solution for a
Z-string
Nielsen-Olesen solution
Higgs field
electromagnetically charged
electromagnetically neutral
They are unstable for reasonable values of .
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Pion String
primordial magnetic fields?
one example of embedded global string

• standard model of strong interaction

QCD phase transition
Below the confinement scale, this model is
described by a sigma model.
four real scalar fields
unstable textures
boundary conditions
pion strings
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Magnetic Field Generationfrom Pion Strings
Brandenberger Zhang, 1999
In case of the pion string, there exists an
interaction between the pion field and the
electromagnetic field.
fine structure constant
Zero mode current appears within the string
core and the azimuthal magnetic field is produced.
string core radius
At the recombination,
present
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Toy Model
MN Brandenberger, 2003
The chiral limit of the QCD linear sigma
model involving the sigma field and the three
pions is employed as an
example.
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Electromagnetic Fields as
Thermal Bath
When the background photon plasma can be regarded
as a thermal bath, the interaction between
charged fields and photon could be included into
the effective potential.
NOTE In order that this method can be justified,
only the photon should be in thermal
equilibrium and other gauge and scalar
fields must not be in equilibrium.
This condition would be satisfied during
a certain regime below the electroweak phase
transition and at least above the
recombination.
If the Lagrangian is thermally averaged, the
first order term of photon field vanishes and the
second order term becomes
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Effective Potential
Thus the vacuum manifold which is at
zero temperature becomes at finite
temperature.
neutral fields
charged fields
By analyzing the stability of such a string
solution under simple assumptions, the
destabilization temperature can be calculated as
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Numerical Simulation
Four scalar fields are evolved numerically on a
three-dimensional lattice by means of a
equation of motion with .
In order to reduce the field fluctuations so that
it is easier to see whether the string
configuration is preserved or not, a damping term
is introduced.
box size, spatial resolution, time step
Basic results are insensitive and the conclusion
is unchanged.

• evolution of field strength and winding
• number of a translation symmetric string

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The time evolution of the spatial distribution of
neutral field and charged field amplitude, and
the winding number for neutral fields starting
from an initial state where a single string
exists in.

• initial condition

• winding
• number

• spatial average of scalar fields

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neutral fields
charged fields
Fig.2
Fig.1
( almost identical)
Fig.3
Fig.4
Fig.5
Fig.6
Fig.5,6
Fig.1-4
averaging 2-dim. volume
i.e. the whole box
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Fig.1
neutral field
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Fig.2
charged field
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Fig.3
neutral field
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Fig.4
charged field
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Fig.5
neutral field
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Fig.6
charged field
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Axenides Perivolaropoulos, 1997
Core Phase Transition
Even when the region where the scalar field
strength is zero disappears, it can be
interpreted that this means a kind of phase
transition that the scalar field has a finite
expectation value at the string core, not a
string decay.
finite temperature effect domination
sufficiently low temperature
neutral field
charged field
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Core Radius Broadening
In the numerical simulations, the core size, R ,
within which the charged fields have a finite
amplitude becomes larger until it reaches
.
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Superconductivity
After the core phase transition, charged
fields have finite expectation value and the
phase has a spatial gradient along the string so
that the electric current will be generated.
current amplitude
Davis Shellard, 1989
loops
vorton
infinite strings
Infinitely long strings and/or loops of large
curvature radius could show a filament-like
spatial distribution feature.
astrophysical counterparts gravitational lensing?
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• 3-dimensiocal simulation

A initially translation symmetric string
evolution is solved in a 3-dimensional box and
the distribution of shows the winding number
appears in some cases.
The probability of winding number appearance is
20.
periodic boundary
when the winding number exists.
when there is no winding number.
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(No Transcript)
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Mao, Li, MN, Zhang Huang, 2005
Signal of Pion Stringat High Energy Experiment
Pion strings can be produced in LHC Pb-Pb
collision at energy 5.5 TeV. They are unstable
and decay into neutral pions and sigma mesons
then into all kinds of pions.
,
,
volume
temperature
,
initially 600 MeV
phase transition 170 MeV
frictional regime

• momentum spectra

Fig.1

freeze out 120 MeV
large decay width of sigma

• total pions

correlation length
Fig.2

• neutral pion

Fig.3
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ltpgt143 MeV
Fig.1
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ltpgt153 MeV
ltpgt178 MeV
decay width of sigma
Fig.2
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ltpgt21 MeV
Fig.3
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Summary

• Some of defects predicted by particle physics
  model
• must be diluted in order to avoid cosmological
  difficulties.

• monopole problem
• domain wall problem

• Some of cosmological and astrophysical problems
• can be solved by defects.

• baryon asymmetry problem
• origin of galactic and intergalactic magnetic
  field

• Embedded defects constructed by electrically
• neutral fields can be stabilized by charged
  plasma.

• Numerical simulations confirm the core phase
  transition,
• the value of destabilization temperature,
• and the superconductivity.

• Stabilized pion strings could be seen at LHC
  experiments.