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

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

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

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 = ± Baryons  b = ± density critical density  Radiation ( CMB, T=2.726±0.005 o K )  r = 4.7 x 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 if m   6 x (<m  ev)  mass  +  rel +  vac

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

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

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

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)

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

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

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

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,

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

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~ new Sn Ia -- z>1.25

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

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

University of Durham Institute for Computational Cosmology 1000 million light years

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

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

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

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 

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

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

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

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

University of Durham Institute for Computational Cosmology

University of Durham Institute for Computational Cosmology

University of Durham Institute for Computational Cosmology

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

University of Durham Institute for Computational Cosmology The origin of cosmic structure QUANTUM FLUCTUATIONS: Inflation (t~ 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)

University of Durham Institute for Computational Cosmology The microwave background radiation

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

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

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~ 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

University of Durham Institute for Computational Cosmology The acoustic peaks in the CMB Wayne hu If M<M jeans the photon-baryon fluid oscillates  of CMB acoustic peak  sound horizon at t rec

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

University of Durham Institute for Computational Cosmology The CMB

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

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

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

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

University of Durham Institute for Computational Cosmology Evolution of spherical perturbations

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