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Exam. Final Exam: * Tuesday Dec 9 th @ 9am E2-229 EIT Complex * 2 hours. Only Specified Calculators! Recall notice from Faculty of Science: could end up with F-DISC in the course. (Can do questions without calculator.). ~70 questions in 2 hours About 10 math questions

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  1. Exam Final Exam: * Tuesday Dec 9th @ 9am E2-229 EIT Complex* 2 hours Only Specified Calculators! Recall notice from Faculty of Science: could end up with F-DISC in the course. (Can do questions without calculator.) • ~70 questions in 2 hours • About 10 math questions • About 10 B&W images – reminds you of colour images in ppt slides • Need to be able to do ratios of masses, timescales, convert units • Based on material from last test onward – everything AFTER Sun • But includes previous material that is referred to in this section of the course.

  2. Tips for exam • Practise (examples) • Rsch • determining stellar radius given luminosity & temperature (e.g. compared to sun) • determining distance using Inverse Square Brightness Law (e.g. compare to stars) • Hubble Law • lifetime on MS

  3. Tips for Exam: recall – used to measure mass in planet using orbiting moon • Do this for a galaxy to determine its dynamical mass in Msun • look up a galaxy online or in textbook (e.g. the Milky Way) • find out orbital velocity • do for 2 radii: • radius of its 21 cm gas layer. • radius of sun for MW • remember to convert units!

  4. Lecture 31: Cosmology 2MASS Observations – colour code on radial velocity • Upcoming: • Various models of the Universe • Life on other worlds • e.g. Drake Equation Learn the material in the lectures. Much of it is NOT in the textbook. Use the textbook for reference. • Homogeneous: the same everywhere • Isotropic: the same in all directions

  5. How galaxies trace the universe: z == Redshift • Hubble’s Law v = Ho * distance • Galaxies in general are are receding from us!  The universe is expanding.

  6. The Past – e.g. wind the film backwards A note about infinity and boundedness. -- an example of unbounded object that is finite. Expand the universe from this past. • infinitely curved spacetime. •  fuzzy singularity where laws of physics breakdown. • no time – spt is bounded in past.

  7. The Big Bang: • Jim Peebles – award winning Princeton cosmologist; undergraduate degree from University of Manitoba. • Following quotes are from Scientific American articles. • That the universe is expanding and cooling is the essence of the big bang theory. You will notice I have said nothing about an "explosion"--the big bang theory describes how our universe is evolving, not how it began.

  8. The Big Bang: Cosmologist Jim Peebles no centre  • It is somewhat misleading, however, to describe the expansion as some type of explosion of matter away from some particular point in space. • That is not the picture at all: in Einstein's universe the concept of space and the distribution of matter are intimately linked; the observed expansion of the system of galaxies reveals the unfolding of space itself. • An essential feature of the theory is that the average density in space declines as the universe expands; the distribution of matter forms no observable edge. no edge 

  9. Evidence: LSS • homogeneous & isotropic • galaxies not distributed as if in an explosion (not schrapnel).

  10. Evidence: CMBR Almost perfect black body. Miniscule flucuations. • Cosmic Microwave Background (CMB) Radiation (CMBR) • Black body: 3 Degree K (e.g. WMAP and Planck missions). • cosmologically redshifted emission from hot plasma Recall the photon on the spt surface.

  11. Formation of Structure in the Universe as it Expands: • Use fluctuations in CMBR as initial conditions in cosmological simulations. • a few * 1/10000 K fluctuations (i.e. 300 micro Kelvin) • exaggerated in plots & bright blobs slightly denser than average

  12. ESA Planck/Herschel Mission – Canadian Participation

  13. ESA Planck Mission • Milky Way removed

  14. Formation of Structure in the Universe as it Expands: • As universe stretches, galaxies that are close together simultaneously feel gravitational pull on each other & Hubble expansion  Matches observations of Large Scale Structure

  15. Observations & Theory: • Input info from observations into computer simulation. • Evolve simulation through time. • See if simulation & observations match.

  16. Observations Computer Simulations Visualization of 3. CMBR Early times MS Now LSS Clustering of Galaxies

  17. Formation of Structure in the Universe as it Expands: 0.21 Gyr after Big Bang

  18. 1 Gyr after Big Bang

  19. ~5 Gyr after Big Bang

  20. 13.6 Gyr after Big Bang  now

  21. Visualization: Cosmological Dark Matter Halos Paul Bode Cosmological Simulation Leo Blitz et al. Milky Way Satellites

  22. Millenium Simulation • http://www.youtube.com/watch?v=74IsySs3RGU

  23. ESA Planck Mission • Milky Way removed • Results in 2014/5. • flucuations in T correspond to “anisotropies” in mass (densities)

  24. Planck & DM • Uses gravitational lensing effects on CMB • note overall homogeneity & isotropy

  25. ESA Planck Mission Highlights

  26. HST DM map Uses redshift of lensing galaxies & plots their DM distribution at redshift.

  27. Past & Future: Past Credit: Nature Journal

  28. The Era of Reionization Dwarf galaxies help light up the cosmic web • http://www.sdsc.edu/News%20Items/PR070814_galaxies.html

  29. Past & Future: Past Credit: Nature Journal

  30. Inflation – a theory • Why homogeneous & isotropic? • Perhaps universe went through a phase change & inflated • Theorists propose an era of unchecked cosmic expansion • Era of Inflation

  31. Inflation – a theory needs evidence • inflation occurs before era of CMB • “last scattering surface” • before CMB photons scatter on particles • CMB when photons can escape between particles • can find imprint on CMB? • EM waves can have aligned orientations == polarization

  32. CMB & Polarization Vectors • Boomerang balloon experiment. • black vectors give direction of polarization.

  33. Inflation – a theory needs evidence • if inflation, then have gravitational waves which twist polarization angle since waves should have a screw motion.

  34. E-mode pattern is symmetric, reflecting physical conditions of matter density enhancements. • B-mode pattern indicates that the light has been twisted by gravitational wave. Implies inflation. • Difficult to separate these modes on CMB

  35. Microwave Inflation Experiments: • BICEP2 (South Pole Station) claimed to see B-modes. • not agree with Planck measurements • seems BICEP2 scientists didn’t remove foreground emission (MW) correctly • POLARBEAR (Atacama Desert) shows can isolate B-modes from CMB polarization pattern. • We don’t know yet!

  36. Discuss cosmology with your neighbour. What do you find the most intriguing thing about it? Which is the most challenging concept for you?

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