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Cosmological Distances Intro Cosmology Short Course Lecture 3 Paul Stankus, ORNL

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Freedman, et al. Astrophys. J. 553, 47 (2001) Riess, et al. (High-Z) Astron. J. 116 (1998) W. Freedman Canadian Modern Hubble constant (2001) A. Riess American Supernovae cosmology (1998) Two Modern Hubble Diagrams Generalize velocity redshift distance magnitude

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Einstein Equivalence Principle Any small patch of GR reduces to SR Albert Einstein German General Theory of Relativity (1915) x t x t General Curved SpaceMinkowski Space x’ t’ For x ’ constant “Proper time” For t’’ constant Proper distance x’’ t’’ ?

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What was the distance to that event? Photons Us t t now Robertson-Walker Coordinates Past Event Coordinate Distance Co-Moving Distance A B Well-defined… but is it meaningful? E NB: Distance along photon line Galaxies at rest in the Hubble flow

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Three definitions of distance Co-Moving/ Coordinate AngularLuminosity Photons t Emitted a(t0)a(t0) Observed Robertson-Walker Coordinates h d Angular Euclidean: h d Define: d Angular h/ Euclidean: F I/4 d 2 Define: d Lum 2 I/4 F t0t0 d Luminosity Intensity I Flux F

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t Physical Radius a(t 0 ) Robertson-Walker Coordinates t x Physical Radius x Newton/Minkowski Coordinates I F I F t0t0 t1t1 Us Flat

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Astronomical Magnitudes Rule 1: Apparent Magnitude m ~ log(Flux Observed a.k.a. Brightness ) Rule 2: More positive Dimmer Rule 3: Change 5 magnitudes 100 change in brightness Rule 4: Absolute Magnitude M = Apparent Magnitude if the source were at a standard distance (10 parsec = 32.6 light-year)

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Some apparent magnitudes 0 -5 -10-20 -15-255 10 15 20 25 SunFull MoonVenusSaturn Ganymed e Uranus Neptune Pluto Mercury Mars Jupiter Sirius Canopus Veg a Deneb Gamma Cassiopeiae Andromeda Galaxy Brightest Quasar Naked eye, daylightNaked eye, urbanNaked eye Ground-based 8m telescope x100 Brightness (Source: Wikipedia)

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Extended Hubble Relation d Lum z Proxy for log(d Lum ) Magnitudes and Luminosity Distances

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t 0 Big Bang t t 0 Now Flat Recall from Lec 2 More generally (all cosmologies): Weinberg 14.6.8

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Today’s big question: Slope = Hubble constant

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Generic 00 Extended Hubble d L z Open

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2.512 in brightness Generic 00 Open Generic 00 Open

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