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Sumario del Cursillo I. Historia Termica y Expansion del Universo II.“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 CDM - Galaxias Espirales:; el crecimiento de discos - La Via Lactea: Propiedades principales - Hoyos negros supermasivos: la evidencia

Sumario del Cursillo

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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 - PowerPoint PPT Presentation

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Page 1: Sumario del Cursillo

Sumario del Cursillo

I. Historia Termica y Expansion del Universo

II. “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 CDM - Galaxias Espirales:; el crecimiento de discos - La Via Lactea: Propiedades principales - Hoyos negros supermasivos: la evidencia

Page 2: Sumario del Cursillo

I. La Expansion del Universo

1. Breve historia termica del Universo2. Formalismo fisico de la expansion3. Sumario de los parametros cosmologicos

Page 3: Sumario del Cursillo

A simpleton’s history of the Universe. IA simpleton’s history of the Universe. I

• t = 0 (?) BB, getting down to business

Planck Era 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

Page 4: Sumario del Cursillo

A simpleton’s history of the Universe. IIA 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

Page 5: Sumario del Cursillo

pp

p p

p4He

Primordial NucleosynthesisPrimordial Nucleosynthesis

e+

2H

3He

3He

4 4 11H H 44He + 2 e+ + 2 He + 2 e+ + 2 + + radn.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)

Page 6: Sumario del Cursillo

The baryonicmass densityfraction of theUniverse is

b ~ 0.03-0.04

Page 7: Sumario del Cursillo

A simpleton’s history of the Universe. IIIA 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

Page 8: Sumario del Cursillo

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” 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 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

Page 9: Sumario del Cursillo

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~os2. 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 Li4. Las caracteristicas (estadisticas) de la estructura en gran escala del Universo5. La noche es oscura (… y tiritan, brillantes, los astros a lo lejos)

Page 10: Sumario del Cursillo

Go to expansion.pdf in Cosmology 1

Page 11: Sumario del Cursillo

- Assume the Universe is homogenous (of density ) and isotropic

- Consider two comoving observers:

l (t) l (to)

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

Taking the time derivative of l (t):

)()()()(

)()()()( tltHtl

ta

tatltatl o

)()()( otltatl

Where H(t) is referred to as the Hubble parameter

Page 12: Sumario del Cursillo

G1

G2

- One of the observers (G1) sends a signal of wavelength em , at time t , to the other

- G2 receives the message at time

ctlttt /)(- Suppose l(t) is small, so that ctl )(

- The signal is received by G2 at the wavelength

emobs

where)(

)(

)(

)(/)(

ta

tat

ta

tactl

em

If the time of G2 is ttto (now),

1)(

)(1

ta

taz o

em

obs

is the redshift

Page 13: Sumario del Cursillo

+l (t)

m

The motion of a mass m with respect toan observer O can be separated in twocomponents:(1)that produced by the mass within the sphere centered on O, with radius l(t)(2) that produced by all mass outside that sphereO

The gravitational effect produced by aspherically symmetric density distributioncentered on O, within an empty cavity alsocentered on O, is null within that cavity

The gravitational effect produced bya spherically symmetric density distributionof radius R, outside of R, is equal to thatof a point containing all the mass within R

lmGlGMmtlm )3/4(/)( 2 The Equation ofMotion of m is then:

Page 14: Sumario del Cursillo

lmGlGMmtlm )3/4(/)( 2 3)](/)()[()( tatatt oo As the Universe expands:

Choosing units so that a(to)=1, and defining o= (to) :

Remember that )()()( otltatl

)(/)3/4()( 2 taGta oMultiplying both sides by da/dt and re-organizing:

0)3

8( 2

a

Ga

dt

d o

Integrating:

03

8 022 a

Gkca

where k is an integration constant

Page 15: Sumario del Cursillo

03

8 022 a

Gkca

NOTE THAT:

1. If o > 0 , then a non-empty Universe cannot be static

2. If k < 0 , then

0)( ta

03/8 2 kcaGa o 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:

2max 3/8 kcGa o

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.

Page 16: Sumario del Cursillo

Expansion in the Flat Model

If k = 0 3/82/1oGaa which can be rewritten as

dtGdaa o 3/8 and integrated to

3/23/22/1 ])3/8)(2/3[()( tGta o

The Universe expands forever: 3/2)( tta but the expansion rate 3/12/1)( tata

tends to zero as t infinity

Rewrite , remembering that and3)](/)()[()( tatatt oo

)(/)()( tatatH so that

G

tHcritflat

8

)(3 2

Current estimates:Ho = 70 km s-1 Mpc-1

crit= 9 x 10 -29 g cm-3

Page 17: Sumario del Cursillo

The Universeis Flat:

= 1

The current expansion rate is Ho = 70 km/s/Mpc

WMAP

Page 18: Sumario del Cursillo