Cosmology 1

1. Cosmology1

2. Topics • Early Milestones in Cosmology • The Expanding Universe • Summary

3. Where Do We Come From? What Are We? Paul Gauguin (1897) Where Are We Going? Museum of Fine Arts, Boston

4. Early Milestones in Cosmology 1823 – Heinrich Olbers • An infinite universe of infinite age contains infinitely many stars. • Therefore, if you look in any direction in the sky, eventually, your line of sight would intercept the surface of a star.

5. Early Milestones in Cosmology Olbers’ Paradox • Since every direction leads to a star, the sky should be as bright as the surface of a star! • So why is the sky dark?

6. Early Milestones in Cosmology 1848 – Edgar Allan Poe • The universe may be infinitely large but be of finite age. • If so, light has not yet reached us from the most distant stars. • This would create so many dark gaps between the nearer stars that the sky would appear dark.

7. Early Milestones in Cosmology Henrietta Leavitt Annie Cannon Harvard College Observatory

8. Distance & Magnitude luminosity(W) distance(m) flux(W/m2) f L d For the Sun f☼=1300W/m2 L☼ = 400 trillion trillion W

9. Distance & Magnitude Astronomers measure brightness using the magnitude scale. This is defined so that a magnitude difference of 5 equals a flux difference of 100 d L m m☼ =-26.8 a = 2.54 x 10-8 W/m2

10. Distance & Magnitude The absolute magnitude M of an object is defined to be its magnitude if it were at a distance of dM = 10 pc = 10-5Mpc d L m 1 parsec (pc) = 3.26 ly = 3.08 x 1016 m

11. Extra Credit Eq. (1) Starting with Eq. (1), derive the distance modulus Due: Friday, 11 April

12. Distance & Magnitude Along with the luminosity distance d, astronomers also measure distances using the distance modulus defined as m = m – M d L m

13. Luminosity-Period Relation L-P Relation of Cepheid Variables Henrietta Leavitt 1912

14. Red-Shifts of Nebulae Vesto M. Slipher (1875 – 1969) In 1912, he announced a puzzling discovery: the light from many nebulae was red-shifted, that is, shifted to the red end of the spectrum z = (lo – le )/ le Lowell Observatory, Flagstaff, Arizona

15. The Nebulae Drawing by the Earl of Rosse 1840s

17. Early Milestones in Cosmology Published 25 November, 1915 Bending of light Prediction: 1.74’’ Karl Schwarzschild Sir Arthur Eddington Eclipse Expeditions 1919

18. Early Milestones in Cosmology Einstein His new theory of gravity, general relativity, predicted that: • The universe must be either expanding or contracting. • However, like his contemporaries, Einstein rejected this prediction in favor of a static universe. Later, he would describe this as the biggest mistake of his life.

19. Discovery: The Expanding Universe Edwin Hubble, 1929 Speed (km/s) Distance (Mpc) 1 Mega-parsec (Mpc) 3.26 x 106 light years (ly)

20. The Expanding Universe 1929 – Hubble’s Law Hubble assumed that the red shift is caused by the motion of galaxies away from us. In this case z = v / c His observations are summarized in Hubble’s Law v = H0 d whereH0 is called Hubble’s constant.

21. The Expanding Universe Hubble’s Law v = H0 d The Hubble Time d = v t d = H0 d t t = 1/H0 For H0 = 70 km/s/Mpc t ~ 14 billion years

22. t1 = past l1 t0 = now d1 d0 t2 = future a0 = 1 lo d2 a2 > 1 The Expanding Universe 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

23. t0 = now d0 lo The Expanding Universe Consider the time derivative of d(t) = a(t) d0 Newton’s dot notation The Hubble parameter This is Hubble’s law

24. d0, t0 L = c (t0 – t1) d1, t1 How Far Is Far ? t0 – t1is called the look-back time

25. Summary • In 1929, Hubble discovered that the red-shifts of galaxies increased roughly linearly with distance • He interpreted these observations as evidence of an expanding universe, summarized in the law v = H0 d • This was predicted by Einstein’s theory of gravity some years earlier. But Einstein did not accept the prediction at the time