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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

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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%

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

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Big-Bang (Theory) Robertson-Walker metric a ( t ) scale factor k Perfect-fluid stress tensor energy density p pressure T diag( , p, p, p )

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

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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

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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 ):

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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

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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):

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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

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Distance-Redshift Relation

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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

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Hubble’s Discovery Paper - 1929 s

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

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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!

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Supernova Taxonomy

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

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

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

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apparent magnitude [log(distance)] Type Ia Supernova

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residuals (magnitudes) Type Ia Supernova

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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

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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) MM Einstein-de Sitter flat, matter-dominated model (maximum theoretical bliss) Astier et al. (2006) SNLS

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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

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Dark Matter

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Temperature of the Universe 100 error bars

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Angular Power Spectrum

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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

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

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

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Angular Power Spectrum k = 0.989 0.012 WMAP

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QSO 1937-1009 Ly Burles et al. Tytler Baryons B h

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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)

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

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

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

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Power Spectrum Tegmark

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cmb dynamicsx-ray gas lensing simulations power spectrum TOTAL (CMB) M B MMMM

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cmb dynamicsx-ray gas lensing simulations TOTAL (CMB) M Subtraction TOTAL M power spectrum

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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%

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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

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