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Olbers' Paradox Astro 101 Fall 2013 Lecture 12 Cosmology T. Howard Cosmology = study of the Universe as a whole • ? What is it like overall? • ? What is its history? How old is it? • ? What is its future? • ? How do we find these things out from what we can observe? • In 1996, researchers at the Space Telescope Science Institute used the Hubble to make a very long exposure of a patch of seemingly empty sky. Q: What did they find? A: Galaxies “as far as The eye can see …” (nearly everything in this photo is a galaxy!) 40 hour exposure What do we know already (about the Universe) ? • Galaxies in groups; clusters; superclusters • Nearby universe has “filament” and void type of structure • More distant objects are receding from us (light is redshifted) • Hubble’s Law: V = H0 x D (Hubble's Law) Structure in the Universe What is the largest kind of structure in the universe? The ~100-Mpc filaments, shells and voids? On larger scales, things look more uniform. 600 Mpc Olbers’ Paradox • Assume the universe is homogeneous, isotropic, infinte, and static • Then: Why don’t we see light everywhere? Why is the night sky (mostly) dark? Olbers’ Paradox (cont’d.) • We believe the universe is homogeneous and isotropic • So, either it isn’t infinite OR it isn’t static • “Big Bang” theory – universe started expanding a finite time ago Given what we know of structure in the universe, assume: The Cosmological Principle On the largest scales, the universe is roughly homogeneous (same at all places) and isotropic (same in all directions). Laws of physics are everywhere the same. Hubble's Law might suggest that everything is expanding away from us, putting us at center of expansion. Is this necessarily true? If there is a center, there must be a boundary to define it => a finite universe. If we were at center, universe would be isotropic (but only from our location) but not homogeneous: Finite volume of galaxies expanding away from us into...what, empty space? Then part of universe has Us galaxies and part doesn’t. But if we were not at center, universe would be neither isotropic nor homogeneous: Us So if the CP is correct, there is no center, and no edge to the Universe! Best evidence for CP comes from Cosmic Microwave Background Radiation (later). The Big Bang At time zero, all separations were infinitely small. Universe then expanded in all directions. Stars, galaxies formed as expansion continued. All galaxies now moving away from each other. A galaxy twice as far away from us, is moving twice as fast (Hubble's Law). So, how old is the Universe? Reversing the Hubble expansion, all separations go back to zero. How long ago? H0 gives rate of expansion. Assume H0 = 75 km / sec / Mpc. So galaxy at 100 Mpc from us moves away at 7500 km/sec. How long did it take to move 100 Mpc from us? distance We can do this same time = velocity calculation for 100 Mpc galaxies at other distances, = 7500 km/sec getting a similar answer. Age of universe is related to H0. Note, H0 may be = 13 billion years in range 65 – 75 km/sec/Mpc (Experts note that this time is just 1 ). H 0 The faster the expansion (the greater H0), the shorter the time to get to the present separation. Redshift vs. “Lookback Time” • Astronomers (and physicists) denote redshift by “z” = amount light has shifted relative to its (laboratory, at rest) wavelength = direct measure of speed of recession of distant galaxies z light travel time Age at redshift (Gyr) (Gyr) 0.037 0.5 13.360 0.075 1.0 12.860 0.254 3.0 10.860 0.488 5.0 8.860 1.04 8.0 5.860 1.74 10 3.860 6.54 13 0.860 10.13 13.38 0.480 1 Gyr = 1,000,000,000 years. using H = 70 km/sec/Mpc Time (now) since Big Bang = 13.860 Gyr 0 Flat universe But this is not galaxies expanding through a pre-existing, static space. That would be an explosion with a center and an expanding edge. If CP is correct, space itself is expanding, and galaxies are taken along for the ride. There is no center or edge, but the distance between any two points is increasing. A raisin bread analogy provides some insight: But the bread has a center and edge. Easier to imagine having no center or edge by analogy of universe as a 2-d expanding balloon surface (this is only one possible analogy for our universe’s geometry): Now take this analogy "up one dimension". The Big Bang occurred everywhere at once, but "everywhere" was a small place. (To understand what it would be like in a 2-d universe, read Flatland by Edwin Abbott: www.ofcn.org/cyber.serv/resource/bookshelf/flat10 ) The Cosmic Microwave Background Radiation (CMBR) A prediction of Big Bang theory in 1940's. "Leftover" radiation from early, hot universe, uniformly filling space (i.e. isotropic, homogeneous). Predicted to have perfect black-body spectrum. Photons stretched as they travel and universe expands, but spectrum always black-body. Wien's Law: temperature decreases as wavelength of brightest emission increases => was predicted to be ~ 3 K now. Found in 1964 by Penzias and Wilson. Perfect black-body spectrum at T = 2.735 K. Uniform brightness (and thus temperature) in every direction. Points are data on the spectrum of the CMBR from the COBE satellite (1989). Curve is a black-body spectrum at T=2.735 K. 1% of the “snow” on a blank TV channel is this radiation! All-sky map of the CMBR temperature, constant everywhere to one part in 105 ! For blackbody radiation, this means brightness is very constant too (Stefan’s law). (WMAP satellite) Deviations are -0.25 milliKelvin (blue) to +0.25 milliKelvin (red) from the average of 2.735 Kelvin. The Early Universe The First Matter At the earliest moments, the universe is thought to have been dominated by high-energy, high-temperature radiation. Photons had enough energy to form particle-antiparticle pairs. Why? E=mc2. pair production annihilation At time < 0.0001 sec, and T > 1013 K, gamma rays could form proton- antiproton pairs. At time < 15 sec, and T > 6 x 109 K, electron-positron pairs could form. Annihilation occurred at same rate as formation, so particles coming in and out of existence all the time. As T dropped, pair production ceased, only annihilation. A tiny imbalance (1 in 109) of matter over antimatter led to a matter universe (cause of imbalance not clear, but other such imbalances are known to occur). Primordial Nucleosynthesis Hot and dense universe => fusion reactions. At time 100-1000 sec (T = 109 - 3 x 108 K), helium formed. Stopped when universe too cool. Predicted end result: 75% hydrogen, 25% helium. Oldest stars' atmospheres (unaffected by stellar nucleosynthesis) confirm Big Bang prediction of 25% helium. We are now in a “Matter-dominated” epoch Other Measurements Support the Big Bang Model of the Universe (Detailed Big Bang theory predicts some things we can measure) We can’t “see” all the way to the Big Bang [we see its “echo”] (Now) … < -- Time … (Early Universe) Radiation and Matter “decoupled” Nuclei and electrons combine to form atoms (H, He) More complex atoms form later from fusion This explains CMB Galaxies – form around clumps of Dark Matter ? Opaque Transparent Computer simulations of structure formation around clumps of Dark Matter predict a universe with shapes/sizes very similar to what we observe. Time since Big Bang. Cosmic expansion timelines (1) Big Bang cosmology + Dark Energy, WMAP values Current mass density ratio 0.27 (incl. Dark Matter) Current value of Dark Energy equivalent density ratio, 0.73 H0 ~ 71 km/s-Mpc Era or Event Time Temp Planck Era < 5x10-44 > 1019 GeV Planck transition 5 x 10-44 1019 GeV ** Grand unification era ** Grand unification of forces ends 10-36 1015 GeV Inflation 10-36 to 10-34 1015 GeV ** Electro weak era ** Electroweak era ends 10-11 100 GeV ** Quark era ** Quark era ends 10-5 200 MeV Cosmic expansion timelines (2) Era or Event Time Temp redshift Neutrino decoupling 0.1 s 3 MeV e- e+ annihilation ends 1.3 s 1 MeV n-p ratio frozen 1.8 s 1010 K Deuterium formation begins 176 s 109 K Matter-dominated era begins 55000 year 8920 K z = 3233 ** Matter era ** CMB visible ~300,000 yr 3000 K 1st stars form 200Myr – 1 Gyr 1st galaxies form 1 Gyr – 5 Gyr universal expansion accelerates ~ 7.1 Gyr z= 0.76, R =0.57 Dark Energy dominates ~ 9.5 Gyr z = 0.39, R = 0.72 ** Dark Energy era** Today ~ 13.7 Gyr z = 0, R = 1 The Early Universe Inflation A problem with microwave background: Microwave background reaches us from all directions. Temperature of background in opposite directions nearly identical. Yet even light hasn't had time to travel from A to B (only A to Earth), so A can know nothing about conditions at B, and vice versa. So why are A and B almost identical? This is “horizon problem”. Solution: Inflation. Theories of the early universe predict that it went through a phase of rapid expansion. Separation between two points (m) If true, would imply that points that are too far apart now were once much closer, and had time to communicate with each other and equalize their temperatures. More on Dark Matter • Dark matter thought to be necessary in cosmology theory to explain clumpy distributions of matter massive enough for galaxies to form • Could have been either CDM or HDM • CDM = non-relativistic (speed << c) • HDM = relativistic (speed ~ c) • Usual predictions of CDM candidates require modifications or extensions to Standard Model of particles • Non-baryonic candidates • Neutrinos (neutrino oscillation implies neutrino mass) • WIMPs – hypothetical • Possibly “heavy” neutrinos or something equally exotic • Axions Current Status Dan Hooper - Closing In On Dark Matter Evidence For Dark Matter !Galactic rotation curves
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