General Relativity and Cosmology – Part II I. People a. William and Caroline Herschel b. Friedrich Bessel c. Immanuel Kant d. Vesto Slipher e. Henrietta Leavitt f. Vera Rubin g. Kent Ford h. Edwin Hubble i. Fritz Zwicky j. Sir Arthur Eddington II. Objects a. Cepheids b. Coma Cluster c. Virgo Cluster d. Andromeda, M31 e. Supernovae f. White-brown-red dwarfs, neutron stars, black holes, g. MACHOs, WIMPs h. Dark halo i. Clusters III. Terms a. Event horizon b. Accretion disk c. Wormhole d. Scri-plus, Scri-minus e. Copernican Principle f. Hubble time, Hubble length g. Horizon h. Planck scales i. Chandrasekhar limit j. Baryonic k. Deceleration parameter l. Standard candle m. Lookback time n. Bolometer o. Luminosity, flux p. Big Crunch, Big Freeze, Big Bounce q. Loitering universe r. Benchmark Model s. BBN IV. Schwarzschild Spacetime and Black Holes a. Metric 1 222GM 2 GM 2 2 2 2 2 ds 1 ( c dt ) 1 dr r d sin d c22 r c r b. Schwarzschild radius 2 2dz 2 2 2 c. Embedding Diagrams, ds1 dr r d dr i. Black hole diagrams – Eddington-Finkelstein, Kruskal, Penrose General Relativity and Cosmology – Part II ii. Locate singularities, infinities, draw light cones, null geodesics. d. GR Tests i. Gravitational lensing ii. Precession of Mercury’s Perihelion iii. Orbit Equation, Effective Potential *2 1 2 r GmM E mr 1 2 22r mr r iv. Wormholes – characteristic features V. Cosmology v at() a. Hubble Law: v H r, z , Hubble parameter: Ht() 0 c at() 1 c b. Hubble time: H0 , Hubble length: H 0 t0 dt dt() c. Proper distance d() t c , dt() p 0 p 0 at() pe 1 z te t0 dt d. Horizon distance: d() t c , p 0 at() at()0 e. Red shift parameter: 1z , a ( t0 ) 1. at()e dx2 f. FLRW metric: ds2 dr 2 S() r 2 d 2 , ds2 x 2 d 2 k 1 x2 g. Three types of spaces – flat, sphere, pseudosphere/hyperbolic h. Friedmann Equation 2 2 2 a8 G c i. Ht() 22 a3 R0 a 2 2 2 8Gc ii. 2 H001, H00 2 R0 3 R0 2 H rm,0 ,0 10 iii. 2 4 3 ,0 2 , H0 a a a i. Density parameters 2 3H 3(1w ) i. , c , w w,0a m, r c 8G 5 5 ii. CMB,0 5.0 10 , ,0 0.681 CMB , r,0 8.4 10 iii. m,0 0.3, ,0 0.7 (Benchmark) j. Models i. Curvature Only (What happens? a?, t0 ?, te ? ) ii. Spatially Flat Universes 2/(3 3w ) 2 t 2 1 3 2 t 1. at(), tH00 , ()tH 0 te 3(1 w ) 8Gt0 H00() t t a. Lambda Only: a H0 a a() t e General Relativity and Cosmology – Part II iii. Multiple-Component Universes a da 1. Ht 0 0 rm,0 ,0 a2 1 aa2 ,0 0 2. Determining Epochs, aarm, m , tcrunch , etc. VI. Luminosity L a. Flux f 22 4 S ( r )(1 z ) 2 b. Luminosity distance dLL S ( r )(1 z ), d d ( t0 )(1 z ),[ 0] 9 c. Standard Candles – Cepheids, Supernovae Type Ia - LL4 10 sun f d. Apparent magnitude m 2.5log10 f0 L dL e. Absolute magnitude Mm 2.5log10 5log 10 L0 10 pc VII. Big Bang Cosmology Timeline a. Epochs b. Baryon to photon ratio 5 105 c. (Radiative) Recombination epoch ( z1370, T 3740 K , t 240,000 yr ) p e H d. Photon decoupling ( z1100, T 3000 K , t 350,000 yr ) Thomson scattering ee e. Last scattering surface f. Reionization VIII. Big Bang Nucleosynthesis a. Binding energies p e H 13.6eV p n D 2.22MeV 8 b. Tnuc6 10 K , t nuc 300 s c. He fraction, Y – primordial 24%, max 1/3 d. Beta decay n p e e ( n 890s ) e. Baryon-antibaryon asymmetry IX. Inflation? a. What is inflation? b. Key problems – Flatness, Horizon, Monopole c. Particle Physics Standard Model – Glashow, Weinberg, Salam, Gell-Mann, Higgs Quarks, Baryons, Mesons, Bosons (photons, gluons, W, Z), Leptons d. Phase transitions (loss of symmetry) and unification of forces: electroweak, GUT and TOE, QED, QCD e. e-foldings, X. Dark Matter a. Observational tests GM b. Orbital speeds in spiral galaxies v R.