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UCL Graduate Lectures An Introduction to Cosmology Sarah Bridle A18 2 October 2004

UCL Graduate Lectures An Introduction to Cosmology Sarah Bridle A18 2 October 2004. Lect 1: Global contents and dynamics of the Universe Lect 2: Dark matter clustering and galaxy surveys Lect 3: The cosmic microwave background radiation Lect 4: Gravitational lensing.

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UCL Graduate Lectures An Introduction to Cosmology Sarah Bridle A18 2 October 2004

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  1. UCL Graduate LecturesAn Introduction to CosmologySarah Bridle A182 October 2004 Lect 1: Global contents and dynamics of the Universe Lect 2: Dark matter clustering and galaxy surveys Lect 3: The cosmic microwave background radiation Lect 4: Gravitational lensing

  2. This lecture:Global contents & dynamics of the Universe • The current cosmological model: overview • From Einstein’s field equations to the dynamics of the universe • Observations of H0 • The age of the Universe • Dark matter and baryon content • Dark energy and supernovae

  3. Global Cosmological Parameters • H0Hubble constant: expansion rate v=H0 r • bBaryon content • DMDark matter content • or DE Dark energy content • w(z) Dark energy properties Derived parameters: • m=b+DMTotal matter content • K=1-m-Curvature of Universe

  4. Concordance Model 70% Dark Energy 5% Baryonic Matter 25% Cold Dark Matter

  5. This lecture:Global contents & dynamics of the Universe • The current cosmological model: overview • From Einstein’s field equations to the dynamics of the universe • Observations of H0 • The age of the Universe • Nucleosynthesis • Dark matter • Dark energy and supernovae

  6. The scale factor a • Relative distance between two observers moving with the Hubble flow • In the past, relative to today • ie. Today a=1 • In the past a<1 • (In the future a>1)

  7. Gki = Rki – 1/2 ki R = 8 G Tki 3 (å2 + k) /a2 = 8  G (t) (2a ä + å2 + k) /a2 = -8  G p(t) From Einstein’s field equations to the Freidman equations Einstein’s field eqns G00 = 3/a2 (å2 + k) G = 1/a2 (2aä + å2 + k)  Tki = diag[(t) –p(t) –p(t) –p(t)] = stress-energy tensor + From GR Friedman eqns Just need p() to solve a(t)…

  8. Gki = Rki – 1/2 ki R = 8 G Tki Gki+ gki= Rki – 1/2 ki R + gki = 8 G Tki The cosmological constant Einstein’s field eqns • Predict the Universe is dynamic • ie. expanding or collapsing • Einstein believed the universe was static • Realised that an alternative solution was: • can be used to make the Universe static • The Universe was then found to be expanding • Einstein calls  his biggest blunder, but now popular

  9. 3 (å2 + k) /a2 = 8  G (t) (2a ä + å2 + k) /a2 = -8  G p(t) •  / a-3(w+1) Evolution of density with time • Rearrange the Freidman equations: • to give • d/dt(a3) = -p d/dt(a3) • If p = w  then • a3 d = -(w+1)  3 a2 da • If also w=constant

  10. What is w? • Defined by the equation p = w  • Often called the “equation of state” • Special values: • w=0 means p=0 eg. matter • w=1/3 eg. radiation • w=-1 looks just like a cosmological constant

  11. Tki = diag[(t) –p(t) –p(t) –p(t)] Gki+ gki= Rki – 1/2 ki R + gki = 8 G Tki Dark energy or cosmological constant? • If w=-1 ie. p=- then Tki = gki • Indistinguishable from a cosmological constant • Dark energy could have any w • Could even vary with time

  12. Evolution of the density •  / a-3(w+1) • Matter dominated (w=0): / a-3 • Radiation dominated (w=1/3): / a-4 • Cosmological constant (w=-1):  =constant • Dark energy with w<-1 eg. w=-2: / a3 • Energy density increases as is stretched out! • Eventually would dominate over even the energies holding atoms together! (“Big Rip”)

  13. What is dominant when? Matter dominated (w=0): / a-3 Radiation dominated (w=1/3): / a-4 Dark energy (w~-1):  ~constant • Radiation density decreases the fastest with time • Must increase fastest on going back in time • Radiation must dominate early in the Universe • Dark energy with w~-1 dominates last Radiation domination Matter domination Dark energy domination

  14. Putting it all together • tot = r + m + DE • r = r 0 a-4 since / a-4 and a today is 1 • r0≡ radiation density today • r0 ≡ r0 / crit by definition • Usually 0 is dropped from r0 for simplicity • So r = crit r a-4 • sim m, DE • Therefore: tot = crit [ r a-2 + m a-3 + DE a-3(1+w)] Assuming w for the dark energy is constant

  15. (å/a)2 = H02(r a-2 + m a-3 + DE a-3(1+w)) Most important equation in this lecture: • Putting these together and usingH0≡ (å/a)0: (å/a)2 = 8  G (t) /3 Freidman eqn1 for k=0 (t) = crit [ r a-2 + m a-3 + DE a-3(1+w)] or if w varies with time, “+ DE exp(-3 s1a (1+w(a’))d(ln a’))

  16. 3 (å2 + k) /a2 = 8  G (t) (2a ä + å2 + k) /a2 = -8  G p(t) How does scale factor relate to time? • Then if k=0 (flat Universe) a(3w+1)/2 da = dt Freidman eqns •  / a-3(w+1) Which we just derived • If w>-1 and w=constant then: a / t2/(3(w+1)) • If w=-1: a / e t

  17. Dynamics of the Universe a / t2/(3(w+1)) • Matter dominated (w=0): a / t2/3 • Decelerating • Radiation dominated (w=1/3): a / t1/2 • Decelerating • Cosmological constant (w=-1): a / e t (special) • Accelerating • Where is the transition? • w>-1/3 decelerating • w<-1/3 accelerating

  18. map.gsfc.nasa.gov/ m_uni/101bb2_1.html

  19. 1 c da/a2 D= s 0 H0 (m a-3 + DE a-3(1+w))1/2 Redshift and comoving distance • Definition of redshift gives 1+z = 1/a • See eg. 5.5.1 Longair Galaxy Formation • Comoving distance ≡ D ≡ s c dt / a • Turns out to be very useful • Rearrange to get D = -c a dt/da da • Use (å/a)2 = H02(m a-3 + DE a-3(1+w))

  20. Luminosity & angular diameter distances • Angular diameter distance ≡ DA • Defined such that =r / DA • r=physical size of object • = angular size on sky • DA = D/(1+z) • Luminosity distance ≡ DL • Defined such that S= L / (4  DL2) • S = bolometric flux density • L = bolometric luminosity • DL = D (1+z)

  21. This lecture:Global contents & dynamics of the Universe • The current cosmological model: overview • From Einstein’s field equations to the dynamics of the universe • Observations of H0 • The age of the Universe • Dark matter and baryon content • Dark energy and supernovae

  22. Measurements of the Hubble constant van den Bergh et al Sandage, Tammann Rob Kennicutt's Evolution of the Hubble constant 1975-1997. This is an updated (10 Mar 97) version of a graph which appeared in Kennicutt R. C., Freedman W. L. & Mould J. R. (1995) ``Measuring the Hubble Constant with the Hubble Space Telescope'', AJ, 110, 1476.

  23. Methods and distance ladder www.astro.gla.ac.uk/ users/kenton/C185/

  24. Hubble Space Telescope Key Project: Hubble constant • Comprehensive study of 5 distance indicators • Freedman et al

  25. 72 §8

  26. This lecture:Global contents & dynamics of the Universe • The current cosmological model: overview • From Einstein’s field equations to the dynamics of the universe • Observations of H0 • The age of the Universe • Dark matter and baryon content • Dark energy and supernovae

  27. 1 da/a t= s 0 H0 (m a-3 + DE a-3(1+w))1/2 The age of the Universe (å/a)2 = H02(m a-3 + DE a-3(1+w)) • Integrate to get: • If w=-1 (so DE=): • If DE=0 (so m=1 given k=0 assumption) • t=s a1/2 da /H0 = 2/ (3 H0)

  28. Measurements of the age of universe • Krauss + Chaboyer • stars age = 12.4 Gyr • estimate ~2 Gyrs min for formation • t0>10.2 Gyr 95 per cent 1-tailed • CMB + flatness -> t0~13.4 Gyr

  29. This lecture:Global contents & dynamics of the Universe • The current cosmological model: overview • From Einstein’s field equations to the dynamics of the universe • Observations of H0 • The age of the Universe • Dark matter and baryon content • Dark energy and supernovae

  30. COMA velocities • Zwicky • ApJ 86, 217 (1937)

  31. Light in COMA suggested ~ 1013 Mo • v ~ 1200 km s-1 -> M ~ 5x1014 Mo • 50 times more mass than expected

  32. Galaxy rotation curves - concept • From redshifts of HI in outer parts of galaxies • velocity should decrease outside star region • Einasto et al. Nature 250, 309 (1974) • Ostriker et al. ApJL 193, L1 (1974) • Rubin, Roberts, Ford ApJ, 230, 35 (1979)

  33. Moore Fig 1 from de Block • Blue: neutral hydrogen, Pink: stars • Right: velocity measured cf predicted

  34. Nucleosynthesis • First few minutes of Universe • Reaction rate propto baryon density squared • He, D, Li tell us physical baryon density • D/H from quasar absorption lines • b h2 =0.02 +/- 0.002 (Tytler, O'Meara) • For h=0.72 (HSTKP) b=0.04 • Even if h=0.6, b<0.06 Not enough! • Must have non-baryonic dark matter

  35. Mike Turner turner_pg7.jpg

  36. Observations of 9 galaxy clusters ~b / m Allen, Schmidt & Fabian 2002

  37. Mass-to-light on larger scales • Bahcall et al 1995 • Claim convergent • Givesm ~ 0.2

  38. Non-baryonic dark matter:plenty of candidates • Hot - Neutrinos • Warm -Sterile neutrinos, gravitino • Cold • LSP (Lightest Super-symmetric Particle, eg. neutralino, axino) • LKP (Lightest Kaluza-Klein particle) • Axions, axion clusters (Rees, Hogan) • Solitons (Q-balls, B-balls) • WIMPs, wimpzilla

  39. This lecture:Global contents & dynamics of the Universe • The current cosmological model: overview • From Einstein’s field equations to the dynamics of the universe • Observations of H0 • The age of the Universe • Dark matter and baryon content • Dark energy and supernovae

  40. Dark Energy • General properties • Cosmological constant or quintessence? • Parameterizing quintessence • Incorporating quintessence into predictions • Parameterizing w(z) • Current measurements • Prospects using supernovae

  41. Dark energy: general properties • The dominant constituent of the universe • Causes accelerated expansion • Modifies growth rate of fluctuations

  42. Cosmological constant or Quintessence? • Cosmological constant: • zero-point quantum fluctuations? factor of 10110 • coincidence of m ~ / why accelerate now? • Quintessence • time-dependent • spatially inhomogeneous • eg. scalar field rolling down a potential • negative pressure - w=pressure/density

  43. Supernovae Ia • Measure expansion rate as fn of z • Systematics? eg. • evolution • grey dust • Tests eg. z=1.7 supernova

  44. Perlmutter et al.

  45. Perlmutter et al.

  46. Dark energy density Barris et al 2004 Dark matter density

  47. Or assume flat universe: Spergel et al 2003

  48. Future supernova data • SNAP satellite proposed • Would measure ~2000 SNIa 0.1<z<1.7 • Funding situation currently uncertain • SNFactory ongoing • To measure ~300 SNIa at z~0.05

  49. To take away from this lecture: • Equations for expansion of Universe as fn of time • Equations for age of Universe • Appreciation of observations of H0, t0 • Qualitative understanding of dark matter problem • Evidence for dark energy from supernovae Next lecture: Dark matter clustering and galaxy surveys

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