1. The Consequences of a Dynamical Dark Energy Density on the Evolution of the Universe By Christopher Limbach, Alexander Luce, and Amanda Stiteler Background image: Andrey Kravtsov., University of Chicago, 2003.

2. Presentation Overview Amanda Stiteler –Introduction –Theory Chris Limbach –Assumptions –Verification of Methods Alex Luce –Results –Conclusion Image by Martin Altmann, Observatory Hoher List, 1997.

3. The Big Bang in Brief

4. Einstein’s Cosmological Model R ij = Ricci tensor R = curvature scalar g ij = space-time metric tensor G = Newton’s gravitational constant T ij = stress-energy tensor Λ = cosmological constant

5. The Friedmann Equation a = dimensionless scale factor ρ R = relativistic matter density ρ M = non-relativistic matter density ρ Λ = dark energy density k = curvature of the universe c = speed of light l 0 = present distance between two galaxies

6. Quintessence Equation relating the scalar field,, and its potential, : Energy density of the scalar field: Evolution of the scalar field:

7. Free Parameters and Parameters which characterize potential Chosen such that V( φ ) mimics nearly constant Λ at present

8. Purpose of this Project Compare the evolution of a universe with constant dark energy density to one with variable dark energy densityCompare the evolution of a universe with constant dark energy density to one with variable dark energy density Determine restrictions of the constants κ and αDetermine restrictions of the constants κ and α Image by NASA., 2006.

9. Assumptions Homogeneous, Isotropic Universe (from WMAP) Total Density = Critical Density Initial Conditions for Ω R, Ω M, Ω Λ from WMAP No Spatial Curvature

11. Method 4 th Order Runge-Kutta Equations Solved:

12. Numeric Solutions Time Relative to Present [Gyrs] Scale Factor a 1 0 0.01 “Time of Big Bang” t

13. Verification h= 0.02 h = 0.01 h = 0.005 Time From Present [Gyrs] Scale Factor 1 Solution error δ h t a h= time step

15. Simulation Results Constant Dark Energy vs. Time Dependent Dark Energy? Restrictions on Free Parameters of Model

16. Dark Energy: Constant Radiation Plays Large role at early times Matter Increases as radiation dies off Dominated by Dark Energy at later times

17. Dark Energy: Time Dependent Dominated by Dark Energy at early times Again dominated by Dark Energy at later times Kappa and Alpha were chosen to agree w/ observations Amount of radiation is relatively lower

18. Dark Energy: Constant vs. Time Dependent

19. Free Parameters Constrained by Age of Universe

20. Scale Factor Represents relative expansion of universe Independent of Free Parameters which characterize expansion

21. Power Law Model of Time Dependent dark energy: Possible Free Parameters do not influence Dynamical behaviour WMAP findings: Universe is >13.7 billion years old

22. Acknowledgments Dimitrios Psaltis Chi Kwan Chan Drew Milsom

23. Sources Cited Kravtsov, Andrey. “Computer-generated image of the distribution of dark matter.” Image from “Cosmologists to plot strategy for dark energy research campaign at Chicago workshop Sept. 17-20.” 3 Sept 2003. 29 April 2007.. Limbach, Christopher, Alexander Luce, and Amanda Stiteler. “The Consequences of a Dynamical Dark Energy Density on the Evolution of the Universe.” 5 Dec 2006. 29 April 2007.. NASA. “WMAP picture of the infant universe.” Image from “Ringside Seat to the Universe’s First Split Second.” 20 March 2006. 30 April 2007.. National Taiwan Science Education Center. “The origin and the evolution of the Universe.” Image from “The Emergence of the Cosmos.” 29 April 2007.. WMAP. “Geometry of the Universe.” “Image from “Sachs-Wolfe Effect.” 2 May 2007..

24. Free Parameters Constrained by Age of Universe

25. Energy Density