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

2. 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

3. 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’’ ?

4. 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

5. 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

6. 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

7. 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)

8. 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)

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

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

11. Today’s big question: Slope = Hubble constant

12. Generic 00 Extended Hubble d L  z Open

13.  2.512 in brightness Generic 00 Open Generic 00 Open