~ (cur+ m + r + v ) ~ R-n ~(1+z)n ~ T n Cosmological Observations in a Curved in addition to Evolving Universe Finding faint Supernovae Calibrating “St in addition to ard Bombs”

~ (cur+ m + r + v ) ~ R-n ~(1+z)n ~ T n Cosmological Observations in a Curved in addition to Evolving Universe Finding faint Supernovae Calibrating “St in addition to ard Bombs” www.phwiki.com

~ (cur+ m + r + v ) ~ R-n ~(1+z)n ~ T n Cosmological Observations in a Curved in addition to Evolving Universe Finding faint Supernovae Calibrating “St in addition to ard Bombs”

Geenen, Mark, Founder and President has reference to this Academic Journal, PHwiki organized this Journal AS 4022: Cosmology HS Zhao Online notes: star-www.st- in addition to .ac.uk/~hz4/cos/cos.html star-www.st- in addition to .ac.uk/~kdh/cos/cos.html Final Note in Library Summary sheet of key results (from John Peacock) take your own notes (including blackboard lectures) Observable Space-Time in addition to B in addition to s See What is out there In all Energy b in addition to s Pupil Galileo’s Lens 8m telescopes square km arrays Radio, Infrared optical X-ray, Gamma-Ray (spectrum) COBE satellites Ground Underground DM detector Know How were we created XYZ & T Us, CNO in Life, Sun, Milky Way, further in addition to further first galaxy first star first Helium first quark Now Billion years ago first second quantum origin The Visible Cosmos: a hierarchy of structure in addition to motion “Cosmos in a computer”

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Observe A Hierarchical Universe Planets moving around stars; Stars grouped together, moving in a slow dance around the center of galaxies. Galaxies themselves some 100 billion of them in the observable universe— as long as m galaxy clusters bound by gravity as they journey through the void. But the largest structures of all are superclusters, each containing thous in addition to s of galaxies in addition to stretching many hundreds of millions of light years. are arranged in filament or sheet-like structures, between which are gigantic voids of seemingly empty space. The Milky Way in addition to Andromeda galaxies, along with about fifteen or sixteen smaller galaxies, as long as m what’s known as the Local Group of galaxies. The Local Group sits near the outer edge of a supercluster, the Virgo cluster. the Milky Way in addition to Andromeda are moving toward each other, the Local Group is falling into the middle of the Virgo cluster, in addition to the entire Virgo cluster itself, is speeding toward a mass known only as “The Great Attractor.” Cosmic Village

Introducing Gravity in addition to DM (Key players) These structures in addition to their movements can’t be explained purely by the expansion of the universe must be guided by the gravitational pull of matter. Visible matter is not enough one more player into our hierarchical scenario: dark matter. Cosmologists hope to answer these questions: How old is the universe H0 Why was it so smooth P(k), inflation How did structures emerge from smooth N-body How did galaxies as long as m Hydro Will the universe exp in addition to as long as ever Omega, Lamda Or will it collapse upon itself like a bubble 1st main concept in cosmology Cosmological Redshift

Stretch of photon wavelength in exp in addition to ing space Emitted with intrinsic wavelength 0 from Galaxy A at time t 1 1st main concept: Cosmological Redshift The space/universe is exp in addition to ing, Galaxies (pegs on grid points) are receding from each other As a photon travels through space, its wavelength becomes stretched gradually with time. Photons wave-packets are like links between grid points This redshift is defined by: E.g. Consider a quasar with redshift z=2. Since the time the light left the quasar the universe has exp in addition to ed by a factor of 1+z=3. At the epoch when the light left the quasar, What was the distance between us in addition to Virgo (presently 15Mpc) What was the CMB temperature then (presently 3K)

Lec 2: Cosmic Timeline Past Now Trafalgar Square London Jan 1 Set your watches 0h:0m:0s Fundamental observers H H H H H H H H A comic explanation as long as cosmic expansion 3 mins later Homogeneous Isotropic Universe He He

A1 A2 A3 B1 B2 B3 R(t) d Feb 14 t=45 days later d C1 C2 C3 D1 D2 D3 2nd Concept: metric of 1+2D universe Analogy of a network of civilization living on an exp in addition to ing star (red giant). What is fixed (angular coordinates of the grid points) what is changing (distance). Analogy: a network on a exp in addition to ing sphere . Angle 1 Exp in addition to ing Radius R(t) 1 2 3 4 1 3 2 4 Angle 1 Fundamental observers 1,2,3,4 with Fixed angular (co-moving) coordinates (,) on exp in addition to ing spheres their distances are given by Metric at cosmic time t ds2 = c2 dt2-dl2, dl2 = R2(t) (d2 + sin2 d2)

3rd Concept: The Energy density of Universe The Universe is made up of three things: VACUUM MATTER PHOTONS (radiation fields) The total energy density of the universe is made up of the sum of the energy density of these three components. From t=0 to t=109 years the universe has exp in addition to ed by R(t). Eq. of State as long as Expansion & analogy of baking bread Vacuum~air holes in bread Matter ~nuts in bread Photons ~words painted Verify expansion doesn’t change Nhole, Nproton, Nphoton No Change with rest energy of a proton, changes energy of a photon VACUUM ENERGY: MATTER: RADIATION:number of photons Nph = constant

The total energy density is given by: log R Radiation Dominated Matter Dominated Vacuum Dominated n=-4 n=-3 n=0 Key Points Scaling Relation among Redshift: z, expansion factor: R Distance between galaxies Temperature of CMB: T Wavelength of CMB photons: lambda Metric of an exp in addition to ing 2D+time universe Fundamental observers Galaxies on grid points with fixed angular coordinates Energy density in vacuum, matter, photon How they evolve with R or z If confused, recall the analogies of balloon, bread, a network on red giant star, microwave oven Topics Theoretical in addition to Observational Universe of uni as long as m density Metrics ds, Scale R(t) in addition to Redshift EoS as long as mix of vacuum, photon, matter Thermal history Nucleosynthesis He/D/H Structure as long as mation Growth of linear perturbation Origin of perturbations Relation to CMB Hongsheng.Zhao (hz4) Quest of H0 /Omega (obs.) Applications of expansion models Distances Ladders (GL, SZ) SNe surveys Cosmic Background from COBE/MAP/PLANCK etc

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Acronyms in Cosmology Cosmic Background Radiation (CBR) Or CMB (microwave because of present temperature 3K) Argue about 105 photons fit in a 10cmx10cmx10cm microwave oven. [Hint: 3kT = h c / ] CDM/WIMPs: Cold Dark Matter, weakly-interact massive particles At time DM decoupled from photons, T ~ 1014K, kT ~ 0.1 mc^2 Argue that dark particles were non-relativistic (v/c 1), hence “cold”. Massive (m >> mproton =1 GeV) Acronyms in addition to Physics Behind DL: Distance Ladder Estimate the distance of a galaxy of size 1 kpc in addition to angular size 1 arcsec [About 0.6 109 light years] GL: Gravitational Lensing Show that a light ray grazing a spherical galaxy of 1010 Msun at typical b=1 kpc scale will be bent ~4GM/bc2 radian ~1 arcsec It is a distance ladder SZ: Sunyaev-Zeldovich effect A cloud of 1kev thermal electrons scattering a 3K microwave photon generally boost the latter’s energy by 1kev/500kev=0.2% This skews the blackbody CMB, moving low-energy photons to high-energy; effect is proportional to electron column density. the energy density of universe now consists roughly Equal amount of vacuum in addition to matter, 1/10 of the matter is ordinary protons, rest in dark matter particles of 10Gev Argue dark-particle-to-proton ratio ~ 1 Photons (3K ~10-4ev) make up only 10-4 part of total energy density of universe (which is ~ proton rest mass energy density) Argue photon-to-proton ratio ~ 10-4 GeV/(10-4ev) ~ 109

Brief History of Universe Inflation Quantum fluctuations of a tiny region Exp in addition to ed exponentially Radiation cools with expansion T ~ 1/R ~t-2/n He in addition to D are produced (lower energy than H) Ionized H turns neutral (recombination) Photon decouple (path no longer scattered by electrons) Dark Matter Era Slight overdensity in Matter can collapse/cool. Neutral transparent gas Lighthouses (Galaxies in addition to Quasars) as long as m UV photons re-ionize H Larger Scale (Clusters of galaxies) as long as m What have we learned Concepts of Thermal history of universe Decoupling Last scattering Dark Matter era Compton scattering Gravitational lensing Distance Ladder Photon-to-baryon ratio >>1 If confused, recall the analogy of Crystalization from comic soup, Last scattering photons escape from the photosphere of the sun The rate of expansion of Universe Consider a sphere of radius r=R(t) , If energy density inside is c2 Total effective mass inside is M = 4 r3 /3 Consider a test mass m on this exp in addition to ing sphere, For Test mass its Kin.Energy + Pot.E. = const E m (dr/dt)2/2 – G m M/r = cst (dR/dt)2/2 – 4 G R2/3 = cst cst>0, cst=0, cst<0 (dR/dt)2/2 = 4 G ( + cur) R2/3 where cst is absorbed by cur ~ R(-2) Angular Scale measures 0 Angular scale depends mainly on the curvature. Gives ~ 0.8o as long as flat geometry, 0 = M + =1 Precision Cosmology ( From the WMAP 1-year data analysis) Dark Energy Vacuum energy Bubble Cosmology Dark Matter Large-Scale Structure Galaxy Rotation Curves Cluster Dynamics Gravitational Lenses MACHOs -- No WIMPs -- Maybe Modified Gravity MOND , TeVeS

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