Cosmic StringsA Study of the Early Universe
Alexander StameroffJames OBrien
Symmetrical Groups E(3) Hamiltonian Mechanics xyz translations and rotations, conservation is momentum in translation and angular momentum in rotationE(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. 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.
Types of Phase TransitionsFirst Order
Expansion and Collision of Bubbles continue until old phase is gone. collision leads to superposition of bubbles.
Second Order Phase TransitionSmoother continues phase transition process
Topological DefectsStable 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.
Types of Topological DefectsSeveral types including: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 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. Heating a sample to cause it to change phase one can view defects akin to cosmic strings in the early universe.
Formation of Cosmic StringsCausally Separated PhasesDifferent Phase Cells separated by Domain WallsInvariant Point at Node of CellsKibble Mechanism
Evolution of Cosmic StringsIntercomutingLoop RadiationonRadiationCosmological ExpansionThe expansion of the universe will stretch the string because it is gravitationally bound, much like the inflating balloon example.
IntercomutingWhen strings touch they intercomute or exchange ends. Namely they connect together at the point and separate from their parent string. A string can intercomute on itself forming a loop.
RadiationStrings 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.
Evolution of Cosmic Strings in Radiation Era
Evolution in Matter Era
Numerical Simulations to Study StringsUse string code by Bruce Allen and Paul Sheoard (20000 lines of C code).Simulates evolution of stringsTakes 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 TravelPrinceton 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 CitedKibbles, T.W.B. Hindsmarsh, M.B. Cosmic Strings. Blackett Laboratory, Imperial College, London. hep-ph/9411342Gangui, 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. .Roberts, Sherrill. Quantum Strangeness and Space-Time. April 27, 2005. .Cambridge Cosmology. Cosmic Strings and Other Topological Defects. 27 April, 2005. .Cosmology in the Labarotory. 27 April, 2005. http://www.phy.syr.edu/research/randomsurfaces/condcos/condcos.html>.