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Cosmology 2

Cosmology 2. Topics. Recap Age of the Universe The Friedman Equation Summary. Discovery: Expansion of the Universe Edwin Hubble, 1929. Speed (km/s). Distance (Mpc). 1 Mega-parsec (Mpc) 3.26 x 10 6 light years (ly). t 1 = past. l 1. t 0 = now. d 1. d 0.

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Cosmology 2

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  1. Cosmology2

  2. Topics • Recap • Age of the Universe • The Friedman Equation • Summary

  3. Discovery: Expansion of the Universe Edwin Hubble, 1929 Speed (km/s) Distance (Mpc) 1 Mega-parsec (Mpc) 3.26 x 106 light years (ly)

  4. t1 = past l1 t0 = now d1 d0 t2 = future a0 = 1 lo d2 a2 > 1 Recap a1 < 1 d1 = a1 d0 l1= a1 lo z = (lo - l1) / l1 1 + z = 1/a1 = 1/a(t1) a(t) is calledthe scale factor

  5. Recap The Hubble law with H0 ~ 70 km/s/Mpc implies a timescale for the expansion of 14 Gy. Is this timescale reasonable?

  6. The Age of the Universe The universe is surely older than the solar system, therefore, the age of the latter provides a lower bound on the age of the universe. We can measure the age of the solar system by measuring the isotopic ratios of meteorites. Assumptions: 1.Meteorites formed along with planets and, 2., the present isotopic ratios of meteorites is, in part, the result of radioactive decay, 3, the initial isotopic ratios were the same for all meteorites

  7. 238U0 206Pb0 238U 206Pb The Age of the Universe Initial composition of 238U and 206Pb Present composition of 238U and 206Pb lead from decay of uranium

  8. 238U0 206Pb0 238U 206Pb The Age of the Universe Given that we can rewrite as

  9. 238U0 206Pb0 238U 206Pb The Age of the Universe In practice one measures isotopic ratios; for example: R238 = 206Pb/204Pb. Note: The amount of 204Pb does not change

  10. 238U0 206Pb0 238U 206Pb The Age of the Universe Unfortunately, we don’t know the initial isotopic ratio 206Pb0 / 204Pb. But, by assumption it is the same for different meteorites, a and b. Therefore, it will cancel in the difference

  11. 238U0 206Pb0 238U 206Pb The Age of the Universe Meteorites that contain 238U also contain the isotope 235U, so the procedure can be repeated for the decay, via a chain, of 235U to 207Pb.

  12. 238U0 206Pb0 238U 206Pb The Age of the Universe We now take the ratio of the differences

  13. 238U0 206Pb0 238U 206Pb The Age of the Universe Using the measured isotopic ratios of lead, the measured isotopic ratio 235U/238U = 7.25x10-3, and the decay rates l(235) = 1/1.015 Gy and l(238) = 1/6.45 Gy, of 235U and 238U, respectively, one finds t = 4.6 Gy. Therefore, the universe must be at least this old

  14. The Twin Towers Quantum Mechanics General Relativity de Broglie Schrödinger Bohr Einstein Heisenberg

  15. Pioneers of the Big Bang Theory Alexander Friedman 1888 - 1925 Georges Lemâitre, 1927

  16. http://www.atlasoftheuniverse.com/galgrps.html

  17. The Cosmological Principle APM Galaxy Survey, Steve Maddox, Will Sutherland, George Efstathiou & Jon Loveday

  18. The Friedman Equation In Newtonian physics, the total energy of a particle of mass m is M d where M = (4/3)p d3 r is the mass within the sphere of radius d and mass density r. m Rearranging, we get

  19. The Friedman Equation For an expanding universe M and the expansion speed at the location of the particle, relative to the center of the sphere is d m m Therefore,

  20. The Friedman Equation Alexander Friedman derived the analogous equation from general relativity M d m The constant K is the curvature of space. We shall consider the case K = 0, only; that is, spaces in which the geometry of space is flat

  21. M d m The Friedman Equation If one compares the Friedman equation for flat spaces with that derived from Newton’s laws K = 0 describes a universe whose total energy is zero!

  22. M d m The Friedman Equation We can rewrite the Friedman equation as where is the critical density is the density parameter and

  23. M d m The Friedman Equation For matter only For radiation only For vacuum energy only For matter + vacuum energy

  24. M d m Extra Credit Solve Friedman’s equation for matter only radiation only and vacuum energy only Due date, Wednesday, April 16 Note: when t = t0, the time at the present epoch, a(t) = 1

  25. Summary • The expansion scale inferred from Hubble’s law ~ 14 Gy is consistent with the lower bound given by the age of the solar system • The scale factor a(t), as a function of cosmic time, can be found by solving the Friedman equation • A universe with a flat geometry (K = 0) is one whose total energy may be taken to be zero

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