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Cosmology 1

Harrison B. Prosper Florida State University YSP 2012. Cosmology 1. Topics. Island Universes The Expanding Universe The Universal Scale Factor Models of the Universe Summary. Island Universes. 1924 – Edwin Hubble

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Cosmology 1

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  1. Harrison B. Prosper Florida State University YSP 2012 Cosmology 1

  2. Topics • Island Universes • The Expanding Universe • The Universal Scale Factor • Models of the Universe • Summary

  3. Island Universes 1924 – Edwin Hubble Measured the distances to several galaxies and showed that they are immense star systems very far from Earth

  4. Island Universes Luminosity-Period Relation of Cepheid Variables Henrietta Leavitt 1912 She deserved, but did not get, a Nobel Prize

  5. The Expanding Universe 1929 – Red Shift Drawing on his own observations and those of others, Edwin Hubble discovered that the red shift, z = (λo - λe) / λe of the light from distant galaxies increases with distance d. λe = emitted wavelength λo = observed wavelength

  6. The Expanding Universe Hubble’s Law v = H0d The Hubble Time d = vt d = H0dt t = 1/H0 For H0= 70 km/s / Mpc t ~ 14 billion years. 1 Mpc (Mega-parsec) = 3.26 x 106 light years (ly)

  7. t1 = past λe t0 = now d(t1) a < 1 d(t0) t2 = future a = 1 d(t) = a(t) d0 λo d(t2) λe = a(t) λo a > 1 z = (λo - λe) / λe The Universal Scale Factor a(t) is the scale factor of the Universe t is cosmic time

  8. Why Can We Assign a Cosmic Time? We have learned that your now and my now do not coincide as we move relative to each other. However, since our relative speeds are small relative to c, it is a very good approximation to take our nows to be the same. The same is true for galaxies. Their motions relative to space are << c. Consequently, we can assign each galaxy approximately the same cosmic time.

  9. Models of the Universe General Relativity Einstein’s theory describes the evolution of spacetime. It can therefore be used to describe the evolution of the Universe The Cosmological Principle (Albert Einstein) The Universe is isotropic (looks the same in all directions) from every vantage point, at all times Such a Universe is necessarily homogeneous, that is, contains matter and energy uniformly distributed

  10. Distribution of Galaxies APM Galaxy Survey, Steve Maddox, Will Sutherland, George Efstathiou & Jon Loveday

  11. Models of the Universe – II TheFriedmann-Lemâitre-Robertson-WalkerMetric This describes a universe in which the proper distance, that is,the distance between two events that are simultaneous (dt = 0), changes with cosmic time, t. The proper distance d(t) between events in the Universe is given by where t0 is the lifetime of the Universe

  12. d0, t0 L = c (t0 – t1) d1, t1 How Far Is Far ? t0 – t1 is the look-back time d0 = d(t0) proper distance between galaxies now d1 = d(t1) proper distance between galaxies then

  13. Models of the Universe – III v The total energy of a galaxy of mass m at a distance d is given by d where M is the total mass enclosed within the sphere of radius d writing gives

  14. Models of the Universe – IV Alexander Friedmann 1888 - 1925 The Friedmann Equation Observations suggest that the curvature constant K = 0, so we can write where

  15. Models of the Universe – V Georges Lemâitre 1927 Assume K = 0 a(0) = 0 and noting that (by convention) a(t0) = 1 Solution

  16. Summary • Expansion of Space In 1929, Hubble discovered the expansion of the Universe. • The Friedmann Equation This equation describes how the scale factor a(t) varies with cosmic time.

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