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Sumario del Cursillo

Sumario del Cursillo. Historia Termica y Expansion del Universo “Cosmologia de Precision”: - La Radiacion de Fondo Cosmico - Los Parametros cosmologicos III. La Estructura de Gran Escala del Universo - La medida de distancias - Velocidades Peculiares de Galaxias

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Sumario del Cursillo

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  1. Sumario del Cursillo • Historia Termica y Expansion del Universo • “Cosmologia de Precision”: • - La Radiacion de Fondo Cosmico • - Los Parametros cosmologicos • III. La Estructura de Gran Escala del Universo • - La medida de distancias • - Velocidades Peculiares de Galaxias • - La Profundidad de Convergencia • IV. Formacion y Evolucion de Galaxias • - El Modelo de “Infall” • - El paradigma de LCDM • - Galaxias Espirales:; el crecimiento de discos • - La Via Lactea: Propiedades principales • - Hoyos negros supermasivos: la evidencia

  2. La Expansion del Universo • Breve historia termica del Universo • Formalismo fisico de la expansion • Sumario de los parametros cosmologicos

  3. A simpleton’s history of the Universe. I • t = 0 (?) BB, getting down to business • PlanckEra T > 1032 K (“size of the Universe” < 10-33 cm) • Theory of Quantum Gravity not available. Strange things happen. • t = 10-43 sec to t = 10-35 sec 1032 K > T > 1027 K • Grand Unified Era • Gravity and “Grand Unified Force” separate • Several competing theories to describe GUF • t = 10-35 sec to t = 10-11 sec 1027 K > T > 1015 K • Hadron Era • Grand Unified Force separates into Nuclear and Electroweak Force •  Inflation (10-35 sec to 10-33 sec  Universe expands by factor of 1050) • Makes geometry Flat; Quarks and antiquarks (hadrons) are created: • 109+1 quarks for every 109 antiquarks; • 109+1 leptons for every 109 antileptons

  4. A simpleton’s history of the Universe. II • t = 10-11 sec to t = 10-2 sec 1015 K < T < 1011 K • Lepton Era • Electroweak force separates into Electromagnetic and Weak • Quarks and anti-quarks annihilate, lone quark out of 109 remains • Universe now dominated by leptons (electrons, positrons, neutrinos, anti- ) • t = 10-2 sec to t = 1011 sec 1011 K < T < 105 K • Radiation Era • - Electrons and positrons annihilate, lone e- out of 109 remains • - Neutrinos decouple from electrons  Cosmic Neutrino Background • - Radiation dominates energy density of the Universe • - t = 1 sec to t = 200 sec  Primordial Nucleosynthesis • Beta decay favors protons over neutrons: • at t = 10 sec there are 7 protons for every neutron, T = 109 K

  5. p p n e+ 4He 2H p 3He p p 3He g Primordial Nucleosynthesis 4 1H  4He + 2 e+ + 2 n + g radn. Within 3 minutes, all neutrons get locked up in Helium nuclei: 25% of all baryonic matter is He, remaining 75% is free protons (Hydrogen)

  6. The baryonic mass density fraction of the Universe is Wb ~ 0.03-0.04

  7. A simpleton’s history of the Universe. III • t = 1011 sec to t = 1016 sec 105 K < T < 10 K • Matter Era • - As Universe expands, elm. energy density drops faster than matter • energy density  matter becomes dominant • - At t = 1013 sec (~370,000 yrs) electrons and protons combine to • form Hydrogen atoms  Matter and Radiation decouple •  Cosmic Microwave Background (CMB) Radiation “flows free” • - t=370,000 yrs to t=200 Myr  Dark Age • - t ~ 200 Myr  First Stars Form, Re-ionization • - t ~ 1 Gyr  Galaxies form • t = 1 Gyr to …?Dark Energy Era? • - t ~ 9 Gyr  Solar System forms • - t = now – 1 Gyr  Life starts • - t = now – 200,000 yrs  Humans appear • - t = now – 35,000 yrs  Rock Art • - t = now – 6,000 yrs  Writing • - t = now – 50 yrs  Rock and Roll

  8. Universal Expansion • 1664 Newton’s Theory of Gravitation • He realizes the Universe must be infinite to prevent collapse • and that equilibrium is unstable • 1917 Einstein obtains new set of equations of gravitational field (TGR) •  unstable Universe, unless a “cosmological constant L” term is • introduced • 1922-23 Friedman obtains set of expanding solutions of Einstein’s • equations. They are independently obtained by Lemaitre in 1927 • 1929 Hubble discovers universal expansion: v = Ho d • He determines Ho to be ~500 km/s/Mpc  universal age ~ 2 Gyr • Einstein declares introduction of L his “greatest error ever” • late 1940s Gamow, Alpher and Herman postulate existence of • cosmic radiation background with T ~ 5 K • early 1960s Quasars are shown to be at cosmological distances • 1964 Hoyle and Tayler show that He abundance can be explained by • primordial nucleosynthesis • 1965 Penzias and Wilson detect Cosmic Microwave Background radiation • 1992 COBE detects fluctuations in the CMB • 2003 WMAP accurately determines main cosmological parameters

  9. Cuales son las principales bases observacionales de la Cosmologia? • 1. El Universo se expande (1929); • aparentemente la expansion es acelerada (2000…) • … y comenzo’ hace 13.7 billones de an~os • 2. Existe un fondo de radiacion cosmica (1965), • de T=2.73 K y fluctuaciones de caracteristicas • estadisticas bien determinadas a nivel de 1 en 105 • (1992-2003) • 3. La abundancia cosmica de isotopos de H, He y Li • Las caracteristicas (estadisticas) de la estructura • en gran escala del Universo • 5. La noche es oscura (… y tiritan, brillantes, los • astros a lo lejos)

  10. Go to expansion.pdf in Cosmology 1

  11. - Assume the Universe is homogenous (of density r) and isotropic - Consider two comoving observers: As the Universe expands, their distance changes: We refer to a(t) to as the scale factor : homogeneity and isotropy require that a(t) be independent on location and on orientation  a(t) depends only on time l (t) l (to) Taking the time derivative of l (t): Where H(t) is referred to as the Hubble parameter

  12. - One of the observers (G1) sends a signal of wavelength lem , at time t , to the other - G2 receives the message at time G2 - Suppose l(t) is small, so that - The signal is received by G2 at the wavelength where G1 (now), If the time of G2 is is the redshift

  13. The motion of a mass m with respect to • an observer O can be separated in two • components: • that produced by the mass within the • sphere centered on O, with radius l(t) • (2) that produced by all mass outside that • sphere m l (t) + O The gravitational effect produced by a spherically symmetric density distribution centered on O, within an empty cavity also centered on O, is null within that cavity The gravitational effect produced by a spherically symmetric density distribution of radius R, outside of R, is equal to that of a point containing all the mass within R The Equation of Motion of m is then:

  14. As the Universe expands: Remember that Choosing units so that a(to)=1, and defining ro= r(to) : Multiplying both sides by da/dt and re-organizing: Integrating: where k is an integration constant

  15. NOTE THAT: • If ro > 0 , then  a non-empty Universe cannot be static • 2. If k < 0 , then  The Universe expands forever; it is said to be open 3. If k > 0 , there is a time for which da/dt = 0; a(t) reaches a max size: Then it re-collapses. It is said to be closed. 4. The k = 0 case is referred to as the flat case. Let’s look at it in more detail.

  16. Expansion in the Flat Model If k = 0 which can be rewritten as and integrated to  The Universe expands forever: but the expansion rate tends to zero as t  infinity Rewrite , remembering that and so that Current estimates: Ho = 70 km s-1 Mpc-1 rcrit= 9 x 10 -29 g cm-3

  17. WMAP The Universe is Flat: W = 1 The current expansion rate is Ho = 70 km/s/Mpc

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