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Cosmic Inflation and the Arrow of Time

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  1. Cosmic Inflation and the Arrow of Time A. Albrecht UCD P262 Spring 2006

  2. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  3. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  4. Inflation: • Try and solve the following puzzles/features of the Standard Big Bang (SBB) universe: • Flatness • Homogeneity • Monopole • Horizon I.0 What is Cosmic Inflation?

  5. i W a 1 In the SBB, flatness is an “unstable fixed point”: Dominates with time At or The “GUT scale” Require today to 55 decimal places to get I.0 What is Cosmic Inflation?

  6. i Gravitational instability: The Jeans Length Average energy density Sound speed • Overdense regions of size • collapse under their own weight. • If the size is they just oscillate I.0 What is Cosmic Inflation?

  7. i SBB Homogeneity: On very large scales the Universe is highly homogeneous, despite the fact that gravity will clump matter on scales greater than RJeans At the GUT epoch the observed Universe consisted of 1079RJeanssized regions. The Universe was very smooth to start with. NB: Flatness & Homogeneity SBB Universe starts in highly unstable state. I.0 What is Cosmic Inflation?

  8. i SBB Monopoles • A GUT phase transition (or any other process) that injects stable non-relativistic matter into the universe at early times (deep in radiation era, ie Ti =1016 GeV) will *ruin* cosmology: Monopole dominated Universe I.0 What is Cosmic Inflation?

  9. i Here & Now SBB Horizon t=0 1080 causally disconnected regions at the GUT epoch Horizon: The distance light has traveled since the big bang: I.0 What is Cosmic Inflation?

  10. The flatness, homogeneity & horizon features become “problems” if one feels one must explain initial conditions. Basically, the SBB says the universe must start in a highly balanced (or “fine tuned”) state, like a pencil on its point. Must/can one explain this? Inflation says “yes” I.0 What is Cosmic Inflation?

  11. i The Basic Tools of Inflation: Consider a scalar field with: L all space and time derivative (squared) terms If Then Which implies w=-1 Inflation I.0 What is Cosmic Inflation?

  12. i A period of early inflation gives: Flatness: W a 1 Dominates over & during inflation Homogeneity At horizon crossing: Evaluate when k=H during inflation A suitably adjusted potential will give : I.0 What is Cosmic Inflation?

  13. i A period of early inflation gives: Monopoles: W a 1 Dominates over & during inflation (and ) Monopoles are erased I.0 What is Cosmic Inflation?

  14. i Inflation Horizon: Inflation starts Inflation ends Here & Now I.0 What is Cosmic Inflation?

  15. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  16. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  17. Inflation: • An early period of nearly exponential (“superluminal”) expansion set up the “initial” conditions for the standard big bang • Predictions: • total=1 (to one part in 100,000 as measured) • Characteristic oscillations in the CMB power • Nearly scale invariant perturbation spectrum • Characteristic Gravity wave, CMB Polarization etc • etc I.1 Successes

  18. WMAP • total=1 Bennett et al Feb 11 ‘03 I.1 Successes

  19. WMAP • total=1 WMAP Only Tegmark et al astro-ph/0310723 WMAP + SDSS Bennett et al Feb 11 ‘03 I.1 Successes

  20. WMAP • Characteristic oscillations in the CMB power Inflation Temperature Power  “Active” models Adapted from Bennett et al Feb 11 ‘03  Angular scale I.1 Successes

  21. WMAP • Nearly scale invariant perturbation spectrum Bennett et al Feb 11 ‘03 I.1 Successes

  22. WMAP • Characteristic Gravity wave, CMB Polarization etc TxE polarization power Inflation “Active” models Bennett et al Feb 11 ‘03 I.1 Successes

  23. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications III) Conclusions • Cosmic Inflation and the Arrow of Time

  24. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications III) Conclusions • Cosmic Inflation and the Arrow of Time

  25. Generic slow roll inflation • Emerging prospects for high precisions tests |nS’ | |nS’ | B. Gold & AA ‘03 WMAP n Future Ly-alpha ns I.2 Future tests

  26. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  27. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  28.        A.A, Davis Meeting on Cosmic Inflation ‘03 I.3 Theoretical advances

  29. I) Inflation in the era of WMAP • Great accomplishments and exiting future prospects For an “snapshot” view the slides at: inflation03.ucdavis.edu

  30. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  31. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  32. Explained by initial conditions Explains the initial conditions of the cosmos 1) The physical (“thermodynamic”) arrow of time 2) Cosmic Inflation Q: How are these two related? Davies ’83 & ’84, Page ’83 (Nature) II.1 Introduction

  33. Why wonder about arrow of time  inflation? • Understand what we are really trying to accomplish with inflation  more solid foundations • Evaluate “alternatives to inflation” • Window on current hot topics • Fun combination of physics ideas II.1 Introduction

  34. Initial conditions in ”normal Physics”: • - Pose physical question • - Chose initial conditions which best describe “apparatus” • - Calculate and compare with experimental results Initial conditions play supporting role Examples: - Arrow of time - Choice of vacuum in quantum field theory • Cosmic Inflation: Explain cosmic initial conditions using physics Laws of physics play supporting role II.1 Introduction

  35. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  36. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  37. -Macroscopic (or thermodynamic) arrow of time emerges from a combination of: • Dynamical trends or “attractors” • Special initial conditions • Choice of coarse graining -Despite a completely reversible microscopic world NB: Not about “T symmetry” See H.D. Zeh The physical basis of the direction of time II.2 Arrow of time basics

  38. (Taking , gravity unimportant) An Example: Special initial conditions  Dynamical trends or “attractors”  Choice of coarse graining  II.2 Arrow of time basics

  39. Recording/Learning • Harnessing energy (actually “low entropy”) Key roles of the arrow of time: II.2 Arrow of time basics

  40. Key roles of the arrow of time (cont.): • Quantum Measurement Everett  same old “thermodynamic” arrow of time II.2 Arrow of time basics

  41. -Macroscopic (or thermodynamic) arrow of time emerges from a combination of: • Dynamical trends or “attractors” Most Fundamental • Special initial conditions • Choice of coarse graining Entropy, laws of thermodynamics, counting number of states etc: -Ways to quantify the above - “Icing on the cake” II.2 Arrow of time basics

  42. Time 1 Time 2 Time 3 II.2 Arrow of time basics

  43. Now consider : gravity very important A completely different trend/attractor: Gravitational Collapse II.2 Arrow of time basics

  44. (Sbh not as well developed as ordinary entropy, but good enough for our purposes as a way to quantify a dynamical trend.) : gravity very important Equilibrium under gravitational collapse: Black Hole (the state of ultimate collapse) II.2 Arrow of time basics

  45. The Punch Line: The thermodynamic arrow of time originates with the very special initial conditions of the cosmos: The early universe is very homogeneous on scales  very far from Eqm. (= black hole) Penrose Cosmic Microwave Background uniform to one part in 105 II.2 Arrow of time basics

  46. The everyday link to gravitational collapse II.2 Arrow of time basics

  47. The everyday link to gravitational collapse II.2 Arrow of time basics

  48. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  49. I) Inflation in the era of WMAP • I.0 What is Cosmic Inflation? • I.1Successes • I.2 Future tests • I.3Theoretical advances • II) Inflation and the arrow of time • II.1 Introduction • II.2Arrow of time basics • II.3Inflation and the arrow of time • II.4 Implications • II.5 Can the Universe Afford Inflation? III) Conclusions • Cosmic Inflation and the Arrow of Time

  50. Standard inflation spiel begins: Cosmological problems of standard big bang: Universe starts far from dynamical trend: -Flat -Homogeneous -Horizons prevent dynamical explanation Q: How can this fact be explained? But isn’t starting far from the dynamical trend exactly what is required to explain the arrow of time? And when do we ever explain initial conditions anyway? II.3 Inflation and the arrow of time