Cosmic StringsCosmic Strings

A Study of the Early UniverseA Study of the Early Universe

Alexander StameroffAlexander Stameroff

James O’BrienJames O’Brien

Symmetrical Groups Symmetrical Groups

E(3) Hamiltonian Mechanics xyz translations and E(3) Hamiltonian Mechanics xyz translations and rotations, conservation is momentum in rotations, conservation is momentum in translation and angular momentum in rotationtranslation and angular momentum in rotation

E(3) + R with time, conservation is energyE(3) + R with time, conservation is energy Galilean transformations (space-time begins Galilean transformations (space-time begins

here) here) Yet to account for more symmetries in Maxwell's Yet to account for more symmetries in Maxwell's

equations we need Weyl transformation. Mass equations we need Weyl transformation. Mass sets length scale, M = hb/c sets length scale, M = hb/c

conformal group SU(...) conformal group SU(...)

Phase Transitions in Early Universe Phase Transitions in Early Universe

Early universe changed phase several Early universe changed phase several times to present universe. times to present universe.

Like ice changing into water into steam Like ice changing into water into steam during the process of heating.during the process of heating.

Each transition from to a new symmetrical Each transition from to a new symmetrical group leads to the change of the universe. group leads to the change of the universe. Symmetry is also lost. Symmetry is also lost.

One single force separated into several forces, em One single force separated into several forces, em electroweak, strong... constitutes a loss of electroweak, strong... constitutes a loss of symmetry.symmetry.

G → H → ... → SU(3) · SU(2) · U(1) → G → H → ... → SU(3) · SU(2) · U(1) → SU(3) · U(1) SU(3) · U(1)

U(1) U(1) ≡≡ electromagnetism electromagnetism SU(2) · U(1) SU(2) · U(1) ≡≡ electroweak electroweak SU(3) SU(3) ≡≡ strong nuclear force strong nuclear force Gravity not presented here because there Gravity not presented here because there

is no theory (Theory Of Everything) to link is no theory (Theory Of Everything) to link gravity to others.gravity to others.

Types of Phase TransitionsTypes of Phase Transitions

First OrderFirst Order

Expansion and Collision of Bubbles continue until old phase is gone. collision leads to superposition of bubbles.

Second Order Phase TransitionSecond Order Phase Transition

Smoother continues phase transition process

Topological DefectsTopological Defects

Stable forms of matter which remain from Stable forms of matter which remain from a phase transition of the old phase.a phase transition of the old phase.

These topological defects persist trough These topological defects persist trough the phase transition into the next phase.the phase transition into the next phase.

Considered remnants of the old universe.Considered remnants of the old universe.Studying them leads to theories and Studying them leads to theories and

understanding of the composition of the understanding of the composition of the early phases of the universe.early phases of the universe.

Types of Topological DefectsTypes of Topological Defects Several types including:Several types including:

Monopoles - single magnetic charges Monopoles - single magnetic charges Domain walls - two dimensional causal separation between Domain walls - two dimensional causal separation between

space such is seen in ferromagnets.space such is seen in ferromagnets. Textures - when more complicated symmetry groups are Textures - when more complicated symmetry groups are

completely broken.completely broken. Cosmic Strings - one dimensional defects formed when axial or Cosmic Strings - one dimensional defects formed when axial or

cylindrical symmetry is broken. cylindrical symmetry is broken.

Empirical Evidence Empirical Evidence

Though cosmological defects Though cosmological defects are a theory and to produce are a theory and to produce them would require extremely them would require extremely high energy particle high energy particle accelerators and complex accelerators and complex systems similar defects can systems similar defects can be viewed in condensed be viewed in condensed matter systems. matter systems.

Nematic Liquid crystals. Nematic Liquid crystals. Heating a sample to cause it to Heating a sample to cause it to

change phase one can view change phase one can view defects akin to cosmic strings in defects akin to cosmic strings in the early universe. the early universe.

Formation of Cosmic StringsFormation of Cosmic Strings

Causally Separated Causally Separated PhasesPhases

Different Phase Cells Different Phase Cells separated by Domain separated by Domain WallsWalls

Invariant Point at Invariant Point at Node of CellsNode of Cells

Kibble MechanismKibble Mechanism

Evolution of Cosmic StringsEvolution of Cosmic Strings

IntercomutingIntercomutingLoop RadiationonLoop Radiationon

RadiationRadiationCosmological ExpansionCosmological Expansion

The expansion of the universe will stretch the The expansion of the universe will stretch the string because it is gravitationally bound, string because it is gravitationally bound, much like the inflating balloon example. much like the inflating balloon example.

IntercomutingIntercomuting

When strings touch they intercomute or When strings touch they intercomute or exchange ends. Namely they connect together exchange ends. Namely they connect together at the point and separate from their parent at the point and separate from their parent string. string. A string can intercomute on itself forming a loop.A string can intercomute on itself forming a loop.

RadiationRadiation

Strings emit gravitational radiation usually, but Strings emit gravitational radiation usually, but can also emit electromagnetic. Loops will can also emit electromagnetic. Loops will disappear because they will emit all their disappear because they will emit all their radiation. radiation.

Two loops intercomutiong and then Two loops intercomutiong and then decaying. decaying.

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Evolution of Cosmic Strings in Evolution of Cosmic Strings in Radiation EraRadiation Era

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Evolution in Matter EraEvolution in Matter Era

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Numerical Simulations to Study Numerical Simulations to Study StringsStrings

Use string code by Bruce Allen and Paul Use string code by Bruce Allen and Paul Sheoard (20000 lines of C code).Sheoard (20000 lines of C code). Simulates evolution of stringsSimulates evolution of strings Takes into account known equations governing Takes into account known equations governing

mostion and interaction of string networks.mostion and interaction of string networks. Can be calibrated for expanding or static universe.Can be calibrated for expanding or static universe. Can be calibrated for Radation era or Matter era.Can be calibrated for Radation era or Matter era. Runs for 90000 CPU hours on COSMOS, 10 years Runs for 90000 CPU hours on COSMOS, 10 years

real-life. Models in time steps. real-life. Models in time steps.

Time TravelTime Travel Princeton physicist J. Richard Princeton physicist J. Richard

Gott has calculated that Gott has calculated that cosmic strings warp spacetime cosmic strings warp spacetime sufficiently for a spaceship to sufficiently for a spaceship to outrace a light ray, and that outrace a light ray, and that two strings moving past one two strings moving past one another in opposite directions another in opposite directions would change the shape of would change the shape of spacetime to such an extent spacetime to such an extent that, "a spacecraft looping that, "a spacecraft looping around the pair of strings could around the pair of strings could return to its starting point return to its starting point before it had left."(Roberts) before it had left."(Roberts)

Works CitedWorks Cited Kibbles, T.W.B. Hindsmarsh, M.B. “Cosmic Strings”. Kibbles, T.W.B. Hindsmarsh, M.B. “Cosmic Strings”. Blackett Laboratory,

Imperial College, London. hep-ph/9411342 Gangui, Alejandro. “Superconducting Cosmic Strings”. Gangui, Alejandro. “Superconducting Cosmic Strings”. American ScientistAmerican Scientist. .

May-June 2000: 254-263.May-June 2000: 254-263. Morris, Richard. Morris, Richard. Cosmic QuestionsCosmic Questions. New York: John wiley & Sons, Inc. . New York: John wiley & Sons, Inc.

1993.1993. Chase, Scott. Chase, Scott. Gravitational RadiationGravitational Radiation. 27 April, 2005. . 27 April, 2005.

<http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html>.<http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html>. Roberts, Sherrill. Roberts, Sherrill. Quantum Strangeness and Space-TimeQuantum Strangeness and Space-Time. April 27, 2005. . April 27, 2005.

<http://www.strangemag.com/spacetime.html>.<http://www.strangemag.com/spacetime.html>. Cambridge Cosmology. Cambridge Cosmology. Cosmic Strings and Other Topological DefectsCosmic Strings and Other Topological Defects. 27 . 27

April, 2005. <http://www.damtp.cam.ac.uk/user/gr/public/cs_home.html>.April, 2005. <http://www.damtp.cam.ac.uk/user/gr/public/cs_home.html>. Cosmology in the LabarotoryCosmology in the Labarotory. 27 April, 2005. . 27 April, 2005.

http://www.phy.syr.edu/research/randomsurfaces/condcos/condcos.html>.http://www.phy.syr.edu/research/randomsurfaces/condcos/condcos.html>.