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Exploring the Universe: Cosmology, Black Holes, and the Age of the Universe

This lecture explores the age of the universe, cosmology, black holes, and the fundamental characteristics revealed by WMAP data. It also discusses outstanding cosmological questions and the challenges of uniting gravity with quantum mechanics.

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Exploring the Universe: Cosmology, Black Holes, and the Age of the Universe

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  1. Astronomyand CosmologiesWed.18.May 2005, last lecture, Spring 2005, Zita • Age of the universe – finish H workshop • Your questions on Cosmology and the Early Universe • Summative lecture • Black holes and Planck time • Questions for your generation • Looking ahead

  2. Age of the Universe • In the Hubble workshop, you: • found the recession speed and distance to 5 galaxies • plotted speed vs distance • Next, find the • slope = v/d = Hubble constant = H (km/s/Mpc) • age of the universe T = 1/H • Discuss: • assumptions • results using Wendy Freedman’s improved H=71

  3. H=v/d and T=1/H

  4. Your questions on Cosmology and the Early Universe WMAP data reveal fundamental characteristics of the universe:

  5. Cosmological parameters

  6. Shape of the universe

  7. Fate of the universe?

  8. You have learned this quarter: Solar system + gravity Kepler’s and Newton’s laws: Jupiter’s moons and dark matter Light! Milky Way, galaxies, and the Universe Big Bang and 3K background radiation WMAP yields cosmological parameters: shape, density, fate? of universe

  9. You learned about ancient and modern observing techniques, and cosmologies across cultures.

  10. You learned: Gravity holds the solar system together Eclipses … size of the Earth, Moon, and Sun …

  11. You learned: Newton’s 2d law explains why Kepler’s 3d law works F=GmM/r2 yields period2 = 4p2r3/GM Precession of the equinoxes … Heliocentric model …

  12. You found Jupiter’s mass from its moons’ orbit, and discovered dark matter from the motion of stars in our Galaxy

  13. You learned: Light and spectra reveal the temperature, composition, brightness, motion, magnetic fields… of stars

  14. You learned: Our Sun is one of billions of stars in the Milky Way Galaxy

  15. You learned: Our galaxy is one of billions of galaxies in the universe

  16. You learned: The 3K microwave background supports the Big Bang… … and shows the origin of structure in the universe, and the shape, density, and fate of the universe

  17. BUT - how did the universe begin? Quantum fluctuations in the vacuum? One universe? (Anthropic principle) Multiverses? (Lucky chance) Bouncing between Big Bangs and Big Crunches?

  18. BH Limits of understanding Looking out: WMAP and high-Z supernovae Looking back: earliest moment = Planck time Quantum Mechanics vs Gravity Wavelength l of mass M vs size R of black hole

  19. BH 1. Gravitational size of a Black Hole We can use energy conservation* to find the size (Rgrav=Schwartzschild radius) of the event horizon of a black hole with mass M: R * next year in Physics of Astronomy

  20. 2. Quantum mechanical size of a Black Hole The deBroglie wavelength, l, describes the smallest region of space in which a particle (or a black hole) of mass m can be localized, according to quantum mechanics.

  21. 3. Find the Planck mass, Mp If a black hole had a mass less than the Planck mass Mp, its quantum-mechanical size could be outside its event horizon. This wouldn’t make sense, so M is the smallest possible black hole.

  22. 4. Find the Planck length, Lp These both yield the Planck length, Lp. Any black hole smaller than this could have its singularity outside its event horizon. That wouldn’t make sense, so L is the smallest possible black hole we can describe with both QM and GR, our current theory of gravity.

  23. 5. Optional: calculate Planck length and mass These are smallest scales we can describe with both QM and GR.

  24. 6. Calculate the Planck time Consider the time it would take for light to cross the Planck length: Speed = distance / time c = Lp / tp Solve for the Planck time tp:

  25. Planck scales You should find roughly these sizes for the: Planck mass = ~ 3 x 10-8 kg ~ 4 x 10-35 m (A black hole smaller than this could be outside its own event horizon, so QM and gravity are not both consistent at this scale.) ~ 10-43 s (At earlier times, our familiar laws of physics “break down”.)

  26. Outstanding cosmological questions What physics operated before the Planck time? What is gravity? Higgs? Graviton? Other? What is dark matter? Neutrino mass? Wimps? What is dark energy? Why does universe’s expansion accelerate? How to unite gravity with QM? Loop quantum gravity? Superstrings? D-branes? Supersymmetric particles?

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