Cosmic Strings
A Study of the Early Universe
Alexander Stameroff
James O’Brien
Symmetrical Groups
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E(3) Hamiltonian Mechanics xyz translations and
rotations, conservation is momentum in
translation and angular momentum in rotation
E(3) + R with time, conservation is energy
Galilean transformations (space-time begins
here)
Yet to account for more symmetries in Maxwell's
equations we need Weyl transformation. Mass
sets length scale, M = hb/c
conformal group SU(...)
Phase Transitions in Early Universe
Early universe changed phase several
times to present universe.
 Like ice changing into water into steam
during the process of heating.
 Each transition from to a new symmetrical
group leads to the change of the universe.
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Symmetry is also lost.
 One
single force separated into several forces, em
electroweak, strong... constitutes a loss of
symmetry.
G → H → ... → SU(3) · SU(2) · U(1) →
SU(3) · U(1)
U(1) ≡ electromagnetism
 SU(2) · U(1) ≡ electroweak
 SU(3) ≡ strong nuclear force
 Gravity not presented here because there
is no theory (Theory Of Everything) to link
gravity to others.
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Types of Phase Transitions
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First Order
Expansion and Collision of Bubbles continue until old phase is gone.
collision leads to superposition of bubbles.
Second Order Phase Transition
Smoother continues phase transition process
Topological Defects
Stable forms of matter which remain from
a phase transition of the old phase.
 These topological defects persist trough
the phase transition into the next phase.
 Considered remnants of the old universe.
 Studying them leads to theories and
understanding of the composition of the
early phases of the universe.
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Types of Topological Defects
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Several types including:
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Monopoles - single magnetic charges
Domain walls - two dimensional causal separation between
space such is seen in ferromagnets.
Textures - when more complicated symmetry groups are
completely broken.
Cosmic Strings - one dimensional defects formed when axial or
cylindrical symmetry is broken.
Empirical Evidence
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Though cosmological defects
are a theory and to produce
them would require extremely
high energy particle
accelerators and complex
systems similar defects can
be viewed in condensed
matter systems.
Nematic Liquid crystals.
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Heating a sample to cause it to
change phase one can view
defects akin to cosmic strings in
the early universe.
Formation of Cosmic Strings
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Causally Separated
Phases
Different Phase Cells
separated by Domain
Walls
Invariant Point at
Node of Cells
Kibble Mechanism
Evolution of Cosmic Strings
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Intercomuting
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Loop Radiationon
Radiation
 Cosmological Expansion
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The expansion of the universe will stretch the
string because it is gravitationally bound,
much like the inflating balloon example.
Intercomuting
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When strings touch they intercomute or
exchange ends. Namely they connect together
at the point and separate from their parent
string.
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A string can intercomute on itself forming a loop.
Radiation
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Strings emit gravitational radiation usually, but
can also emit electromagnetic. Loops will
disappear because they will emit all their
radiation.
Two loops intercomutiong and then
decaying.
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Evolution of Cosmic Strings in
Radiation Era
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Evolution in Matter Era
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Numerical Simulations to Study
Strings
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Use string code by Bruce Allen and Paul
Sheoard (20000 lines of C code).
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Simulates evolution of strings
Takes into account known equations governing
mostion and interaction of string networks.
Can be calibrated for expanding or static universe.
Can be calibrated for Radation era or Matter era.
Runs for 90000 CPU hours on COSMOS, 10 years
real-life. Models in time steps.
Time Travel
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Princeton physicist J. Richard
Gott has calculated that
cosmic strings warp spacetime
sufficiently for a spaceship to
outrace a light ray, and that
two strings moving past one
another in opposite directions
would change the shape of
spacetime to such an extent
that, "a spacecraft looping
around the pair of strings could
return to its starting point
before it had left."(Roberts)
Works Cited
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Kibbles, T.W.B. Hindsmarsh, M.B. “Cosmic Strings”. Blackett Laboratory,
Imperial College, London. hep-ph/9411342
Gangui, Alejandro. “Superconducting Cosmic Strings”. American Scientist.
May-June 2000: 254-263.
Morris, Richard. Cosmic Questions. New York: John wiley & Sons, Inc.
1993.
Chase, Scott. Gravitational Radiation. 27 April, 2005.
<http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html>.
Roberts, Sherrill. Quantum Strangeness and Space-Time. April 27, 2005.
<http://www.strangemag.com/spacetime.html>.
Cambridge Cosmology. Cosmic Strings and Other Topological Defects. 27
April, 2005. <http://www.damtp.cam.ac.uk/user/gr/public/cs_home.html>.
Cosmology in the Labarotory. 27 April, 2005.
http://www.phy.syr.edu/research/randomsurfaces/condcos/condcos.html>.