# 2. The evolution and structure of the universe is governed by General Relativity (GR).

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1 7/11 Chapter 12 Cosmology Cosmology is the study of the origin, evolution, and structure of the universe. We start with two assumptions: 1. Cosmological Principle: On a large enough scale (large compared to superclusters of galaxies), the universe is homogeneous (the same everywhere) and isotropic (the same in all directions). 2. The evolution and structure of the universe is governed by General Relativity (GR). Recall that GR tells us that matter and energy curve space. The universe contains matter and energy is it curved? There are three possible geometries: 1. Euclidian Geometry zero curvature geometry of a flat surface such as a tabletop. 2. Riemannian Geometry positive curvature geometry of the surface of a sphere. 3. Lobaschevskian Geometry negative curvature geometry of the surface of a saddle. A Euclidian universe is flat (and open). A Riemannian universe is closed. A Lobashevskian universe is open There is a critical density 4 10 g/cm works out to one H atom per cubic meter. If the density of the universe has the critical value, it is flat. If greater, it is closed. If less, open. We define the density parameter is defined to be the ratio of the density of the universe to the critical density. If = 1, open and flat. If > 1, closed and positively curved. If < 1, open and negatively curved. How can we deduce if the universe is flat or curved either positively or negatively? One way is to count galaxies within an angle. If we see fewer galaxies than expected within a given angle, the universe is positively curved. If we see more, it is negatively curved. If we see the number expected, it is flat. The figure on the left is for a flat universe, the center, for a positively-curved universe, and the one on the right, for a negatively-curved universe. Such measurements and others indicate that the universe is flat!

2 This means that should be 1. When we account for all the visible matter in the matter we can detect in the universe, we find = 0.05! Universe should not be flat. Yes but, we haven t included dark matter! We don t know what dark matter is, but we have some ideas. Two main ideas: MACHO and WIMP MACHO MAssive Compact Halo Object These would be objects such as neutron stars, black holes, white dwarfs, brown dwarfs, rogue planets floating around in the halos of galaxies. We can detect these objects using the gravitational lens effect when an object comes between us and a distant object, it will cause the distant object to brighten. We have found some MACHO s, but not enough to account for all the dark matter required to explain the motions of galaxies. WIMP Weakly Interacting Massive Particle Two types of WIMP s hot dark matter and cold dark matter Hot Dark Matter Perfect Candidate neutrinos Two problems:

3 1. Even though there are more neutrinos in the universe than any other type of particle, their masses are too small to account for dark matter needed. 2. Computer models based on hot dark matter do not produce a universe like the one we see around us. Cold Dark Matter Computer models based on cold dark matter do produce a universe like the one we see around us. Problem no particle known to exist has the proper characteristics of cold dark matter. All known particles are detectable. There are hypothetical particles ones that might exist but ones we have yet to find that would fill the bill. 1. Axion The strong nuclear interaction conserves handedness or parity while the weak nuclear interaction does not. The axion is a hypothetical particle that, if it exists, would account for why one does and the other doesn t. 2. Magnetic Monopole We have never found an object with a north magnetic that doesn t also have a south magnetic pole. There is no theoretical reason why we can t have an isolated north or south magnetic pole. They would be very massive and it wouldn t take many to account for the dark matter needed. We have searched and are searching for them, but none have been found. 3. Lowest Mass Supersymmetric Partner What we want is symmetry when we exchange particles with one-half integer spin (call fermions) and particles with integer spin (bosons). Hypothesize that an electron (fermion) has as boson partner called selectron. The photon (boson) has a fermion partner called a photino. These new particles will interact only gravitationally with the rest of the universe. Supersymmetric partners would be much more massive. The lightest of these would be stable and account for dark matter. But, when we add dark matter into its value rises only to 0.25 still too small. New version of the flatness problem. Another problem isotropic nature of the universe. When we measure the temperature of space (cosmic microwave background radiation) in one direction, we get the same value as in the opposite direction. Same temperature in two regions of space that could not possibly have interacted. Need to interact to be in equilibrium. Called the Horizon Problem. Inflation solves the problem to make sense of this, let s go over the history of the universe billion years ago a cataclysmic event occurred called the Big Bang creation event of the universe when space, time, matter, and energy were created. After this event, the universe began to expand, creating more space as it did so.

4 43 2. During the first 10 s (the Planck time) we don t know what happened. Current physics is not sufficient to determine what happened. 3. During this interval, the universe was controlled by a single force that we might call the superforce. At the end of the interval, gravity separated from the superforce leaving behind the grand unified force thus begins the GUTs era. (Grand Unification Theory) Until 10 s, the universe remains in the GUTs era. At the end of this period, the strong nuclear interaction separates from the GUT force leaving behind the electroweak force. 5. What happens here is a tremendous amount of energy given up as occurs when water changes to ice The universe undergoes a phase transition. 6. This outflow of energy causes the universe to rapidly increase its rate of expansion until time 39 about 10 s. During this time the universe increases in size by 43 orders of magnitude by a 43 factor of 10 from smaller than an atomic nucleus to larger than the solar system. 7. This is inflation. 8. The universe slows its expansion to the previous rate at the end of inflation. Solves the horizon problem since before inflation all points in the universe were close enough together to interact came to equilibrium before inflation began and maintained after inflation even though they could no longer interact. Let s us understand why the universe is flat. The universe in getting larger gets flatter just as expanding a basketball to the size of the Earth makes it look flat. 9. At this point the universe is composed of electrons, quarks, neutrinos, photons and dark matter whatever that might be. 10. As the universe cools, it gets to the point where quarks can begin forming neutrons and protons and antiquarks can begin forming antineutrons and antiprotons. Somehow there was some asymmetry between the production of matter and antimatter for every billion antimatter particles created, a billion and one matter particles were created. The billion antimatter particles annihilated a billion matter particles creating photons and leaving behind that single particle of matter those matter particles form the matter in the universe today. 11. Now, the universe is composed of neutrons, protons, electrons, neutrinos, photons, and dark matter. 12. At about three minutes, the universe cools sufficiently that neutrons and protons can come together to form nuclei heavy hydrogen, helium - 3, helium - 4 and some lithium. This process ends about a half hour after the big bang and at this time, by weight, the universe is about 75% H and 25% He. 13. After this, nothing much happens for about 300,000 years. During this time, the universe is composed of electrons, protons, He nuclei, photons and dark matter. The universe is opaque photons don t travel far before they scatter.

5 14. At the end of this time, the temperature of the universe dropped to about 3000 K cool enough for electrons to begin combining with nuclei to form atoms the universe become transparent. 15. These photons of last scattering would show a black body spectrum at 3000 K as the universe expand, it cools and the black body temperature drops. Today, it is just under 3 K. 16. We know the story from here on out with the creation of huge stars, black holes, and galaxies. Supporting Evidence for the Big Bang Theory: 1. It correctly predicts the ratio of H to He in the universe. 2. It correctly predicts the cosmic background radiation.

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