1. PRE-SUSY Karlsruhe July 2007 Rocky Kolb The University of Chicago Cosmology 101 Rocky I : The Universe Observed Rocky II :Dark Matter Rocky III :Dark Energy

2. Dark Matter: 25% Dark Energy (  ): 70% Stars: 0.5% Free H & He: 4% Chemical Elements: (other than H & He)  0.025% Neutrinos: 0.47%  CDM Radiation: 0.005%

3. The Universe Observed Cosmological parameters: Power spectra–characterization of perturbations: “Standard model”: Dark Energy and Dark Matter

4. Big-Bang (Theory) Robertson-Walker metric a ( t )  scale factor k    Perfect-fluid stress tensor  energy density p  pressure T   diag( ,  p,  p,  p )

5. Robertson-Walker Metric If k  0 (spatially flat) (comoving coordinates: dimensionless) (physical distance: increasing dimension of length

6. Robertson-Walker Metric Three curvature  R =  k  a  ( t ) k = +1 finite-volume spherical space ( V   a  ) k  infinite-volume hyperbolic space If k  0 (spatially curved) Value of a ( t ) only enters spatial curvature. Measurables are Ratios such as Changes – Hubble expansion rate – Deceleration parameter

7. Stress-Energy Tensor T  : fluids with different w Conservation of stress energy: Effect of gravity:    depends on metric & derivatives of metric Equation of state parameter: If w  w ( a ):

8. Dark Energy–Cosmological Term Local fluid four-velocity  U  In fluid rest frame for Perfect-fluid stress-energy tensor: Einstein’s 1917 field equations: Move cosmological term to the right-hand side: Identify  G   : Cosmological term  equivalent to (and indistinguishable from) w  component of T 

9. Evolution of H is a key quantity Friedmann equation: From conservation of stress-energy: Define dimensionless fraction of present contribution: Friedmann equation (redshift is proxy from time or scale factor):

10. Evolution of H is a key quantity 1929: Measurement of H today ( H  – Hubble’s constant) sets distance and time scales for the Universe 1998: Measurement of H in the past ( q  – deceleration parameter) evidence for dark energy

11. Distance-Redshift Relation

12. Light travels on ds   can choose  d  Distance-Redshift Relation In small-z limit: H  d L ( z )  z   luminosity-distance ~ distance redshift expressed as Doppler velocity

13. Hubble’s Discovery Paper - 1929 s

14. Riess et al astro-ph/9410054 Hubble’s data

15. Program: measure flux F assume you know luminosity (standard candle) deduce observational luminosity distance d L 2 = L /  F measure redshift z input a model cosmology (  i ) and calculate d L (z) compare to data Distance-Redshift Relation Need a bright standard candle!

17. Supernova Taxonomy

18. The mysterious language of astronomy L  luminosity (calibrated) F  intensity (measured) (e.g., erg s -1 ) (e.g., erg s -1 cm -2 )

19. Luminosity / Solar Luminosity -20 0 20 40 60 days Type I a Supernovae (not calibrated) Supernova Cosmology Project Type Ia Supernova

20. Luminosity / Solar Luminosity Type Ia Supernovae (calibrated) -20 0 20 40 60 days Type Ia Supernova Supernova Cosmology Project

21. apparent magnitude [log(distance)] Type Ia Supernova

22. residuals (magnitudes) Type Ia Supernova

23. 3) age of the universe 4) structure formation High-z SNe are fainter than expected in the Einstein-deSitter model 1) Hubble diagram (SNe) 2) subtraction Astier et al. (2006) SNLS Einstein-de Sitter: spatially flat matter-dominated model (maximum theoretical bliss)  CDM confusing astronomical notation related to supernova brightness supernova redshift z Evidence for Dark Energy The case for  : 5) baryon acoustic oscillations 6) weak lensing 7) galaxy clusters

24. High-z SNe I a are fainter than expected in the Einstein-deSitter model cosmological constant, or …some changing non-zero vacuum energy, or … or some unknown systematic effect(s) MM Einstein-de Sitter flat, matter-dominated model (maximum theoretical bliss)  Astier et al. (2006) SNLS

25. Age of the universe Evolution of H(z) Is a Key Quantity Many observables based on H ( z ) through coordinate distance r(z) Luminosity distance Flux = (Luminosity /  d L  ) Angular diameter distance   Physical size / d A Volume (number counts) N / V  ( z ) Robertson–Walker metric

26. Dark Matter

27. Temperature of the Universe 100  error bars

28. Angular Power Spectrum

29. At recombination, baryon  photon fluid undergoes “acoustic oscillations” Compressions and rarefactions change Peaks in correspond to extrema of compressions and rarefactions Multipole number corresponds to a physical length scale Acoustic Peaks

30. Sound travel distance known Observed l peak ~ geometry Flat (Euclidean) Spherical (closed) Hyperbolic (open)

31. WMAP David T. Wilkinson 1935-2002 WMAP science team WMAP model

32. Angular Power Spectrum  k = 0.989  0.012 WMAP

33. QSO 1937-1009 Ly  Burles et al. Tytler Baryons  B h  

34. M33 rotation curve 10 5 100 50 expected from luminous disk observed galaxy & cluster dynamics gravitational lensing structure formation CMB observations v (km/s) R (kpc)

35. Sofue & Rubin Rotation Curves CO – central regions Optical – disks HI – outer disk & halo

37. Assume there is an average density Expand density contrast in Fourier modes Autocorrelation function defines power spectrum Power spectrum

38. Power spectrum related to rms fluctuations Power spectrum sphere of radius R

39. Power Spectrum Tegmark

40. cmb dynamicsx-ray gas lensing simulations power spectrum  TOTAL    (CMB)  M    B  MMMM

41. cmb dynamicsx-ray gas lensing simulations  TOTAL    (CMB)  M   Subtraction   TOTAL  M   power spectrum

42. Cold Dark Matter: 25% Dark Energy (  ): 70% Stars: 0.5% Free H & He: 4% Chemical Elements: (other than H & He)  0.025% Neutrinos: 0.47%  CDM Radiation: 0.005%

43. PRE-SUSY Karlsruhe July 2007 Rocky Kolb The University of Chicago Cosmology 101 Rocky I : The Universe Observed Rocky II :Dark Matter Rocky III :Dark Energy