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Anisotropic Evolution of D -Dimensional FRW Spacetime

Anisotropic Evolution of D -Dimensional FRW Spacetime. Chad A. Middleton Mesa State College February 19, 2009. Cosmology. is the scientific study of the large scale properties of the Universe as a whole. addresses questions like: Is the Universe (in)finite in spatial extent?

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Anisotropic Evolution of D -Dimensional FRW Spacetime

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  1. Anisotropic Evolution of D-Dimensional FRW Spacetime Chad A. Middleton Mesa State College February 19, 2009

  2. Cosmology is the scientific study of the large scale properties of the Universe as a whole. addresses questions like: • Is the Universe (in)finite in spatial extent? • Is the Universe (in)finite in temporal extent? • What are the possible geometries of the Universe? • What is the ultimate fate of the Universe?

  3. In 1915, Einstein completes hisGeneral Theory of Relativity • describes the curvature of spacetime • describes the matter& energy w/in spacetime

  4. Space is a dynamical structure whose shape is determined by the presence of matter and energy. Matter tells space how to curve Space tells matter how to move “Spacetime and Geometry” by Sean Carroll, 1st edition, Pearson publishing

  5. Cosmological Principle On sufficiently large distance scales, the Universe is 1. Isotropic 2. Homogeneous  Maximally Symmetric Space

  6. For a Homogeneous & Isotropic Universe…… 3 possible Geometries Recent data indicates that the Universe is flat http://en.citizendium.org/images/thumb/1/1e/Omega/ratio/and/cosmological/morphology-990006b.jpg

  7. Friedmann-Robertson-Walker (FRW) Cosmology • Choose the flat Robertson-Walker metric* • Choose a perfect fluid stress-energy tensor * the Robertson-Walker metric describes a spatially homogeneous, isotropic Universe evolving in time

  8. The FRW Equations are… • density () & pressure (p) determine the evolution of the scale factor (a)

  9. Choose an “equation of state” • For radiation: • For pressure-less matter: • For a vacuum:

  10. Density as a function of the scale factor • Radiation dominated: • Matter dominated: • Vacuum energy dominated:

  11. Data from Type Ia Supernovae, WMAP and SDSS implies… • The expansion of the • Universe is ACCELERATING! • The Universe is flat • Seems to indicate a VacuumEnergy http://nedwww.ipac.caltech.edu/level5/Carroll2/Figures/figure3.jpeg http://map.gsfc.nasa.gov/media/060916/060916/320.jpg

  12. The Cosmological Constant Problem From the zero-point energies of vacuum fluctuations… Cosmological observations imply… • Taking the ratio yields.. http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BlackHoleThermo/VirtualPair.gif

  13. The Ultraviolet Catastrophe Consider the energy density, u(λ), of an ideal blackbody... “Modern Physics” by Paul A. Tipler & Ralph A. Llewellyn, 5th edition, W.H. Freeman and Company The resolution of the Ultraviolet Catastrophe led to Quantum Mechanics

  14. A Quantum Theory of Gravity? In QFT, particles are treated as mathematical points.

  15. String Essentials… • Points of QFT  1D Strings • 2 Types  Closed & Open • Different Vibrational Modes  Different particles http://eskesthai.blogspot.com/2006_02_01_archive.html

  16. Compactified Extra Dimensions Non-Compactified Extra Dimensions String Theory demands Extra Dimensions  Two possible descriptions http://www.damtp.cam.ac.uk/user/tong/string.html.jpg http://www.columbia.edu/cu/record/23/18/11c.gif

  17. Kaluza-Klein Compactification Consider a 5D theory, w/ the 5th dimension periodic… http://images.iop.org/objects/physicsweb/world/13/11/9/pw1311091.gif where • Kaluza, Theodor (1921) Akad. Wiss. Berlin. Math. Phys. 1921: 966–972 • Klein, Oskar (1926) Zeitschrift für Physik, 37 (12): 895–906

  18. D-Dimensional FRW Cosmology • Choose the flat Robertson-Walker metric • Choose a perfect fluid stress-energy tensor where is the higher dimensional pressure

  19. D-dimensional FRW field equations

  20. An Incomplete History… • Paul & Mukherjee , “Higher-dimensional Cosmology with Gauss-Bonnet terms and the Cosmological-Constant Problem” Phys. Rev.D42, 2595 (1990) • Mohammedi, “Dynamical Compactification, Standard Cosmology, and the Accelerated Universe” Phys. Rev.D65, 104018 (2002) • Andrew, Bolen, and Middleton, “Solutions of Higher Dimensional Gauss-Bonnet FRW Cosmology”, Grav. And Gen. Rel., Vol. 39, Num. 12 (2007) pps. 2061-2071 • Ito, “Accelerating Universe from Modified Kasner Model in Extra Dimensions”, arXiv: 0812.4326v2 [hep-th]

  21. Choose a 4D and higher dimensional Equation of State Remarkably, the equations decouple…

  22. The FRW field equations become… where

  23. Conclusions This research is a work in progress. To do: • Solve the field equations for special cases (v = w, n = 0, 3 - dn = 0, etc.) • Is there a realistic compactification scenario? • Does this scenario produce a solution for the time evolution of a(t) that agrees with known data? • What does this model say about an early inflationary epoch, if anything? • What does this model say about a late-time acceleration?

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