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Inflation, Dark Energy, and the Cosmological Constant

Inflation, Dark Energy, and the Cosmological Constant. Intro Cosmology Short Course Lecture 5 Paul Stankus, ORNL. L= 0. Recall from Lecture 4:. The Friedmann Equation. GR. yadda, yadda, yadda…. Basic Thermodynamics. Hot. Sudden expansion, fluid fills empty space without loss of energy.

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Inflation, Dark Energy, and the Cosmological Constant

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  1. Inflation, Dark Energy, and the Cosmological Constant Intro Cosmology Short Course Lecture 5 Paul Stankus, ORNL

  2. L=0 Recall from Lecture 4: The Friedmann Equation GR yadda, yadda, yadda…

  3. Basic Thermodynamics Hot Sudden expansion, fluid fills empty space without loss of energy. dE = 0 PdV > 0 thereforedS > 0 Hot Hot Gradual expansion (equilibrium maintained), fluid loses energy through PdV work. dE = -PdVif and only ifdS = 0 Hot Isentropic Adiabatic Perfect Fluid Cool

  4. L=0 No static Universes! Big Bang! The Friedmann Equation Together with the perfect fluid assumption dE=-PdVgives The second/dynamical Friedmann Equation

  5. L=0 Over- Column A Column B B. RiemannGerman G. Ricci-Curbastro Italian Formalized non-Euclidean geometry (1854) Tensor calculus (1888)

  6. Einstein closed, static Universe “The Heavens endure from everlasting to everlasting.” The full Friedmann equations with non-zero “cosmological constant” L Albert Einstein German General Theory of Relativity (1915); Static, closed universe (1917)

  7. Indistinguishable! Cosmological constant as part of General Relativity Space filled by energy of uniform density and P=-r Cosmological “Leftists” vs “Rightists” Left:L as part of geometry Right:L as part of energy&pressure Tmnfor matter and radiation in local rest frame Effective Tmnin the presence of a cosmological constant

  8. Continuum Inflationary Universes What if a flat Universe had no matter or radiation but onlycosmological constant (and/or vacuum energy)? “de Sitter Space” Exponentially expanding! …but yet oddly static:No beginning, no ending, H(t) never changes W. de Sitter Dutch Vacuum-energy-filled universes “de Sitter space” (1917)

  9. Unchanged! E E Negative pressure: not so exotic…. Constant energy density  Negative pressure

  10. Radiation Dominated Inflationary De Sitter Light Cones in De Sitter Space Robertson-Walker Coordinates t (1/H0) Radiation-filled Us Now BB Vacuum-energy-filled c(c/H0)

  11. Radiation Dominated Inflationary De Sitter Inflation solves (I): Uniformity/Entropy Robertson-Walker Coordinates t (1/H0) Alan Guth American Us Now Cosmological inflation (1981) CMB decouples  Inflation BB no inflation  BB with inflation  c(c/H0)

  12. L=0 Inflation Solves (II): Early Flatness (Yet another) Friedmann Equation Non-Flatness grows ~a(t)  Huge increase!? Dominates with increasing a(t), leading to faster increase

  13. L0 Flat (Generic) Open Closed

  14. Horizon Our lonely future? Matter/radiation Dark energy

  15. The New Standard Cosmology in Four Easy Steps Inflation, dominated by “inflaton field” vacuum energy Radiation-dominated thermal equilibrium Matter-dominated, non-uniformities grow (structure) Start of acceleration in a(t), return to domination by cosmological constant and/or vacuum energy. w=P/r +1/3 accdec t -1/3 -1 aeHt at1/2 at2/3 now

  16. Points to take home • For full behavior of a(t), need an equation of state (P/r) • Matter/radiation universes: evolving, and finite age • Cosmological constant L a legal but unneeded piece of GR; L is indistinguishable from constant-density vacuum energy • All L>0 evolve to inflationary (de Sitter) universes; Do we live at a special time? Part 2 • Early inflation solves flatness and uniformity puzzles • Life in inflationary spaces is very lonely

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