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

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%

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

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

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

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

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 ):

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 

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):

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

Distance-Redshift Relation

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

Hubble’s Discovery Paper s

Riess et al astro-ph/ Hubble’s data

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!

Supernova Taxonomy

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

Luminosity / Solar Luminosity days Type I a Supernovae (not calibrated) Supernova Cosmology Project Type Ia Supernova

Luminosity / Solar Luminosity Type Ia Supernovae (calibrated) days Type Ia Supernova Supernova Cosmology Project

apparent magnitude [log(distance)] Type Ia Supernova

residuals (magnitudes) Type Ia Supernova

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

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

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

Dark Matter

Temperature of the Universe 100  error bars

Angular Power Spectrum

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

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

WMAP David T. Wilkinson WMAP science team WMAP model

Angular Power Spectrum  k =  WMAP

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

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

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

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

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

Power Spectrum Tegmark

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

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

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%

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