1. University of Durham Institute for Computational Cosmology Carlos S. Frenk Institute for Computational Cosmology, Durham Galaxy clusters

2. University of Durham Institute for Computational Cosmology Galaxy clusters - Tiajin Carlos Frenk Institute of Computational Cosmology University of Durham Introduction to the large-scale structure of the Universe The formation of dark matter halos The structure of dark matter halos

3. University of Durham Institute for Computational Cosmology What is the Universe made of?

4. University of Durham Institute for Computational Cosmology What is the universe made of? critical density = density that makes univ. flat:  = 1 for a flat univ. (of which stars, Cole etal ‘02 )  s = 0.0023 ± 0.0003 Baryons  b = 0.044 ± 0.004 density critical density  Radiation ( CMB, T=2.726±0.005 o K )  r = 4.7 x 10 -5 Dark matter (cold dark matter)  dm =  0.20 ± 0.04 Dark energy (cosm. const.   =  0.75 ± 0.04   b  dm    (assuming Hubble parameter h=0.7) Neutrinos  = 3 x 10 -5 if m   6 x 10 -2 (<m  ev)  mass  +  rel +  vac

5. University of Durham Institute for Computational Cosmology  m =0.24±0.04 >>  b =0.044±0.004 all matter baryons  Dark matter must be non-baryonic The nature of the dark matter

6. University of Durham Institute for Computational Cosmology Non-baryonic dark matter candidates hotneutrinoa few eV warm ?a few keV cold axion neutralino 10 -5 eV- >100 GeV Type candidate mass

7. University of Durham Institute for Computational Cosmology What is the Universe made of? Dark energy

8. University of Durham Institute for Computational Cosmology Evidence for  from high-z supernovae SN type Ia (standard candles) at z~0.5 are fainter than expected even if the Universe were empty  The cosmic expansion must have been accelerating since the light was emitted a/a 0 =1/(1+z)

9. University of Durham Institute for Computational Cosmology Friedmann equations For a homogeneous & isotropic Universe a = expansion factor, k= curvature  mass  +  rel +  vac

10. University of Durham Institute for Computational Cosmology Evidence for  from high-z supernovae Distant SN are fainter than expected if expansion were decelerating

11. University of Durham Institute for Computational Cosmology Friedmann equations For a homogeneous & isotropic Universe a = expansion factor, k= curvature 2 nd law of thermodynamics: p= pressure Equation of state:  mass  +  rel +  vac

12. University of Durham Institute for Computational Cosmology Friedmann equations where  tot  mass  +  rel +  VAC a -3 a -4 const?  If  VAC =  VAC (z,x) and  quintessence If    vac  const, d  da  0  p  c 2 w  1   Accelerated expansion Expansion accelerates In general,

13. University of Durham Institute for Computational Cosmology Friedmann equations where  At early times the universe is always decelerating  tot  mass  +  rel +   a -3 a -4 const? For matter or radiation:  There must be a transition between decelerating and accelerating expansion

14. University of Durham Institute for Computational Cosmology Supernovae Ia and dark energy Reiss etal ‘04Redshift z  (m-M) (mag) Transition from decelerated to accelerated expansion at z~0.5 16 new Sn Ia -- 6 @ z>1.25

15. University of Durham Institute for Computational Cosmology The large-structure of the Universe

16. University of Durham Institute for Computational Cosmology Results from the “2-degree field” galaxy survey 250 nights at 4m AAT 1997-2002 Anglo-Australian team  221,000 redshifts to b j <19.45 Median z=0.11

17. University of Durham Institute for Computational Cosmology 1000 million light years

18. University of Durham Institute for Computational Cosmology The origin of the large-structure of the Universe

19. University of Durham Institute for Computational Cosmology The beginning of the Universe In 1980, a revolutionary idea was proposed: our universe started off in an unstable state (vacuum energy) and as a result expanded very fast in a short period of time  cosmic inflation

20. Inflation Initially, Universe is trapped in false vacuum Scalar field  Universe decays to true vacuum keeping  v ~ const Universe oscillates converting energy into particles

21. University of Durham Institute for Computational Cosmology  Inflation for beginners At early times k=0. So,  Vac   const.   Universe expands exponentially Inflation ends when  Vac decay and Universe reheats a.  kc 2  8  3 G  a 2 

22. University of Durham Institute for Computational Cosmology Conventional inflation Chaotic inflation Cosmic Inflation t=10 -35 s Inflation theory predicts: 1.Flat geometry (  =1) (eternal expansion) 2.Small ripples in mass distribution

23. University of Durham Institute for Computational Cosmology Quantum fluctuations are blown up to macroscopic scales during inflation Generation of primordial fluctuations Because of quantum fluctuations, different parts of the Universe finish inflating at slightly different times

24. University of Durham Institute for Computational Cosmology Spectrum of inhomogeneities  x

25. University of Durham Institute for Computational Cosmology Standard inflation predicts: 1. FLAT GEOMETRY : 2. Cosmic Inflation

26. University of Durham Institute for Computational Cosmology

27. University of Durham Institute for Computational Cosmology

28. University of Durham Institute for Computational Cosmology

29. Evolution of an adiabatic perturbation in CDM universe M=10 15 M o  =1, h=0.5 Dak matterbaryons radiation Fluctuation amplitude Log a(t)/a 0 Horizon entry

30. University of Durham Institute for Computational Cosmology The origin of cosmic structure QUANTUM FLUCTUATIONS: Inflation (t~10 -35 s) P(k)=Ak n T 2 (k,t) Damping (nature of dark matter) + n=1 Mezaros damping Free streaming P(k) Transfer function R h (t eq ) Hot DM (eg ~30 ev neutrino) - Top-down formation Cold DM (eg ~neutralino) - Bottom-up (hierachical)

31. University of Durham Institute for Computational Cosmology The microwave background radiation

32. z =1000 The microwave background radiation Plasma z =  T=2.73 K 380 000 years after the big Bang inflation

33. University of Durham Institute for Computational Cosmology Temperature anisotropies in the CMB Intrinsic anisotropies at last scattering: Gravitational redshift: Sachs-Wolfe effect Doppler effect Adiabatic perturbations Line of sight effects: Time varying potentials: ISW effect Compton scattering: SZ effect

34. University of Durham Institute for Computational Cosmology The origin of cosmic structure n=1 Mezaros damping Free streaming Large scales P(k) R h (t eq ) Small scales  Hot DM (eg ~30 ev neutrino) - Top-down formation Cold DM (eg ~neutralino) - Bottom-up (hierachical) QUANTUM FLUCTUATIONS: Inflation (t~10 -35 s) P(k)=Ak n T 2 (k,t) Damping (nature of dark matter) + Transfer function Hot DM (eg ~30 ev neutrino) - Top-down formation Cold DM (eg ~neutralino) - Bottom-up (hierachical)  CMB

35. University of Durham Institute for Computational Cosmology The acoustic peaks in the CMB Wayne hu http://background.uchicago.edu/~whu/ If M<M jeans the photon-baryon fluid oscillates  of CMB acoustic peak  sound horizon at t rec

36. University of Durham Institute for Computational Cosmology The cosmic microwave background radiation (CMB) provides a window to the universe at t~3x10 5 yrs In 1992 COBE discovered temperature fluctuations (  T/T~10 -5 ) consistent with inflation predictions The CMB 1992

37. University of Durham Institute for Computational Cosmology The CMB 1992 2003

38. University of Durham Institute for Computational Cosmology WMAP temperature anisotropies in the CMB Bennett etal ‘03

39. University of Durham Institute for Computational Cosmology The Emergence of the Cosmic Initial Conditions curvature total density baryons

40. University of Durham Institute for Computational Cosmology The Emergence of the Cosmic Initial Conditions > 10 5 independent ~ 5  measurements of T are fit by an a priori model with 6 (physical) parameters Best  CDM model has : t o = 13.7±0.2 Gyr h =0.71±0.03  8 =0.84±0.04  t =1.02±0.02  m =0.27±0.04  b =0.044±0.004  e =0.17±0.07 (Bennett etal 03) Parameters in excellent agreement with other data T-P x-corr  Adiabatic fluctns curvature total density baryons

41. University of Durham Institute for Computational Cosmology 1. FLAT GEOMETRY: 2. QUANTUM FLUCTUATIONS: Inflation (t~10 -35 s) adiabatic Dark matter CMB (t~3x10 5 yrs) Structure (t~13x10 9 yrs) The origin of cosmic structure

42. University of Durham Institute for Computational Cosmology Evolution of spherical perturbations

43. University of Durham Institute for Computational Cosmology n=1 damping Free streaming Calculating the evolution of cosmic structure N-body simulation “Cosmology machine”