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Inflation, Dark Energy, and the Cosmological Constant Intro Cosmology Short Course Lecture 5 Paul Stankus, ORNL
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The Friedmann Equation 0 GR Recall from Lecture 4: yadda, yadda, yadda…
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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
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The second/dynamical Friedmann Equation The Friedmann Equation 0 Together with the perfect fluid assumption dE PdV gives No static Universes! Big Bang!
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Over- B. Riemann German Formalized non- Euclidean geometry (1854) G. Ricci- Curbastro Italian Tensor calculus (1888) Column AColumn B 0
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“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
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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!
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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
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Negative pressure: not so exotic…. Constant energy density Negative pressure EE Unchanged!
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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
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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)
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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
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Flat (Generic) 00 Open Closed
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Our lonely future? Horizon Matter/radiationDark energy
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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
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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
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