December 5, 2011 – 10am class

1. December 5, 2011 – 10am class Midterm 3: Wed. Dec. 7 All assignments must be turned in by Wednesday, in class Review for final: Sunday Dec. 11, 6-8pm Final Exam: Wednesday Dec. 14, 10:30am-12:30pm Today: Cosmology

2. Why do we need inflation? The Horizon Problem The Flatness Problem

3. INFLATION is a natural explanation of the HORIZON PROBLEM.

4. The flatness problem Why is space so nearly flat?

5. If Ω were even a tiny bit different than 1, it would by now be WAY different. (Ω=1 means space is flat) So in the early universe, Ω must have been REALLY REALLY nearly 1.

6. “Inflation” of the Universe happened when the Universe had cooled far enough that “symmetry breaking” of the GUT force could occur -- sometimes described as a “phase transition.”

7. According to the current model of inflation: At t≈ 10-34 seconds, the Universe started expanding exponentially, doubling in size every 10-34 seconds. Inflation ended at t≈ 10-32 seconds, after expansion by a factor 1030.

8. Today, the observable universe has a radius r≈ c/H0≈ 4300 Mpc ≈ 1026 meters At the beginning of inflation, it had a radius r≈ 10-30meter At the end of inflation, it had a radius r≈ 1 meter

9. Why did the universe start inflating exponentially (& why did it stop)? According to the particle physicists: The universe underwent a phase transition at t≈ 10-35 seconds.

10. Example of a PHASE TRANSITION: When water goes from liquid to solid, it goes from a random state to an ordered state. Energy is released.

11. During a freeze in Florida, orange trees are sprayed with water. Why? The energy released by freezing water warms the leaves & fruit.

12. NORMAL EXPANSION without INFLATION:

13. Only a small part of the Universe which was within our Horizon just prior to inflation remained in our Horizon after inflation.

14. The huge factor by which the Universe expanded also explains why we’re nearly flat. Here’s a 2D representation of a 3D surface that is nearly flat when expanded.

15. Note that during inflation the radius of curvature of the geometry of the Universe increased effectively faster than the speed of light. But since the expansion was on the geometry of the Universe itself, and not the matter, then there is no violation of special relativity.

16. Our visible Universe, the part of the Big Bang within our horizon, is effectively a `bubble' on the larger Universe. However, those other bubbles are not physically real since they are outside our horizon. We can only relate to them in an imaginary, theoretical sense. They are outside our horizon and we will never be able to communicate with those other bubble universes.

18. Back to the history of the Early Universe: 3.  t=10-38seconds to 10-10 seconds after the big bang:   THE ELECTROWEAK era

19. 4.  10 -10 secondto 0.001 second:  The Particle Era  The Universe was filled with electrons, neutrinos and quarks. Today, protons, anti-protons, neutrons, antineutrons are each made up Of 3 quarks, held together by gluons.  But earlier the Universe was too hot for the quarks to be bound together as protons or neutrons, so we had just the various types Of quarks and gluons running around freely.

20. When the Universe finally cooled for the quarks to form protons, neutrons, etc.  the protons and anti-protons rapidly annihilated, forming photons. If there had been equal numbers of protons and anti-protons, then all there would be left would be photons.

21. BUT…The protons slightly outnumbered anti-protons, so we were left with protons and photons.

22. Today: Photons outnumber protons by a billion to one. There are approximately 400 photons / cm3 currently in the CMBR.

23. 5.  0.001 second to 3 minutes:  The era of NucleosynthesisThe Universe cooled to temperature = 109 K, similar to the core of the Sun. As in the core of the Sun, fusion of hydrogen into helium created a Universe with about 25% helium (by mass), plus very small amounts of deuterium (proton + neutron) and lithium.

24. The exact ratios of Helium/hydrogen, deuterium/hydrogen etc depend on the density of baryons (protons & neutrons) and the temperature of the Universe at during this era. These in turn depend on cosmological parameters such as the expansion rate of the Universe.

25. Helium-4 is measured in by looking at emission lines in spectra of H II regions in dwarf galaxies. Li/H is measured by spectroscopy of old star stellar atmospheres. D/H is measured by looking at quasar absorption lines from distant galaxies. Density of Baryons in Universe In units of critical density

26. (6) t=300,000 years: Recombination. Electrons and protons recombined, the universe Became transparent, and the photons were then free to stream to us.

27. What caused the density fluctuations that we see as temperature Fluctuations of the CMB? There are basically two models: (1) Before inflation, there were quantum fluctuations on subatomic scales which were stretched to astrophysical size during inflation. These fluctuations became density perturbations when the vacuum energy that drove inflation decayed into radiation and matter. (2) The competing theory says that the density perturbations were seeded by topological defects. Depending upon how the symmetry is broken during inflation these defects might be point-like (global monopoles), one-dimensional (cosmic strings), or three-dimensional (spacetime textures).

28. The figure shows a random collection of textures taken from high-resolution, supercomputer simulations. Red indicates a positive twist in the topological charge density and blue a negative twist.

29. It turns out that topological defects create density perturbations which develop significantly later than the quantum fluctuation model, and so there is a signature in the CMB. The current anisotropy data appear to be consistent with inflation and inconsistent with the topological defect scenario

31. Hot /cold Spots in the CMB Observed Predicted, For different Geometries Of the Universe Flat

32. theory CMB temperature fluctuations reality

34. The Future of the Universe References: • The Far and Future Universe: Eschatology from a Cosmic Perspective, 2002 Edited by George F.R. Ellis • A dying Universe: the Long-term fate and evolution of astrophysical objects, by Fred Adams and Gregory Laughlin, 1997 Rev. of Modern Physics, Vol. 69, No. 2. • Time Without End: Physics and Biology in an Open Universe, by Freeman Dyson, 1979, Rev. of Modern Physics, Vol. 51, 447. • The Collapse of the Universe: An Eschatological Study, by Martin Rees, 1969 Observatory 89, 193.

35. Eschatology from the Greek, eschatos = the furthest "Theology. The doctrine of the last or final things, as death, resurrection, immortality, the end of the age, the second advent of Christ, judgment, and the future state."

36. Review If the cosmological constant = 0 (no dark energy) then we can understand the evolution of the Universe in terms of the critical density: If the density of the Universe > the critical density, then the expansion will halt and the Universe will contract (CLOSED UNIVERSE). If the density of the Universe < the critical density, then the Universe will expand forever (OPEN UNIVERSE).

37. Newtonian result (no dark energy, cosmological constant = 0) Ω < 1 Ω = 1 Distance between two galaxies Ω > 1 Time

38. The FUTURE in a CLOSED UNIVERSE: The expansions halts, and the Universe contracts. Eventually the Universe collapses -- the BIG CRUNCH.

39. The closed Universe may "bounce” – the expansion/contraction is cyclic. Or here… Or maybe here You are here

40. Problems with a Cyclic Model • With each cycle the Universe gains energy. • Consider a photon emitted by the Sun today. It goes into intergalactic space, and is redshifted because of expansion, losing energy. Then as the Universe contracts, the photon is blueshifted, gaining energy. It keeps being blueshifted until it is more energetic than it was at the time of emission. • So during contraction, the Universe is hotter than it was at the corresponding time during contraction. • The hot photons heat the dead stars, causing them burn more, explode, or evaporate. • Black holes swallow up more and more matter at the end of the contraction, until the Universe is one large black hole. • What happens next is not well understood -- perhaps the beginning of the next cycle!

41. Entropy Problems with a Cyclic Model – continued (2) Entropy always increases • In Thermodynamics: entropy is the amount of disorder in a system • Second Law of Thermodynamics: Entropy is always increasing!

43. If entropy always increases, then how do low-entropy objects such as eggs form in the first place? • The law of entropy applies to closed systems. It does not forbid decreases in entropy in open systems, including chickens. A hen takes in energy and goes through a great deal of effort to produce an egg.

44. Low entropy High entropy

45. Our psychological sense of time is based on the second law of thermodynamics: Entropy defines the Arrow of Time The Curious Case of Benjamin Button • It summarizes what we have seen, what we have experienced, • what we think will happen. • But the fundamental laws of physics have no preference for a • direction in time. • A theory suggests that entropy-reducing events are possible, but they • always erase any evidence of ever having occurred.

46. Entropy with your coffee. No matter how many times you mix milk into your coffee, you will never see them spontaneously unmix, thanks to the relentless increase in the entropy of the Universe.

47. WMAP results + Type 1a Supernova have suggested that the expansion is accelerating, and that the Universe will expand forever. However, it will be important in the next few years to see if these results can be confirmed in an independent way.