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

2. The Friedmann Equation  0 GR Recall from Lecture 4: yadda, yadda, yadda…

3. Basic Thermodynamics Sudden expansion, fluid fills empty space without loss of energy. dE  0 PdV  0 therefore dS  0 Gradual expansion (equilibrium maintained), fluid loses energy through PdV work. dE  PdV if and only if dS  0 Isentropic Adiabatic Perfect Fluid Hot Cool

4. The second/dynamical Friedmann Equation The Friedmann Equation  0 Together with the perfect fluid assumption dE  PdV gives No static Universes! Big Bang!

5. Over- B. Riemann German Formalized non- Euclidean geometry (1854) G. Ricci- Curbastro Italian Tensor calculus (1888) Column AColumn B  0

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

7. Cosmological “Leftists” vs “Rightists” Left:  as part of geometry Right:  as part of energy&pressure T  for matter and radiation in local rest frame Effective T  in the presence of a cosmological constant Cosmological constant as part of General Relativity Space filled by energy of uniform density and P  Indistinguishable!

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

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

10. Light Cones in De Sitter Space t (1/H 0 ) Now BB Radiation Dominated Inflationary De Sitter  (c/H 0 ) Robertson-Walker Coordinates Radiation-filled Vacuum-energy-filled Us

11. Inflation solves (I): Uniformity/Entropy t (1/H 0 ) Now BB no inflation  Radiation Dominated Inflationary De Sitter  (c/H 0 ) Robertson-Walker Coordinates Us BB with inflation  CMB decouples  Inflation Alan Guth American Cosmological inflation (1981)

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

13. Flat (Generic) 00 Open Closed

14. Our lonely future? Horizon Matter/radiationDark 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/w=P/ -1/3 +1/3 a  e Ht a  t 1/2 a  t 2/3 t now acc dec

16. Points to take home For full behavior of a(t), need an equation of state (P/  ) Matter/radiation universes: evolving, and finite age Cosmological constant  a legal but unneeded piece of GR;  is indistinguishable from constant-density vacuum energy All  >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