1	ASTR 5460, Wed. Apr. 2, 2003 Assignments/Reminders Finish Chapter 7 Longair: Friedman World Models
2	Assignments/Reminders Friday: Astro-ph only 10 minutes or so (stick to title/authors, general area, and why is it interesting or important? Only read enough of papers to address this. Sandage review article: Sey will lead Chapter 8 Longair (cf. Sandage article) Continue to familiarize yourself with these models via on-line cosmology calculators \
3	Sloan Post-starburst Quasars Background in papers/proposals Tasks Identify from the SDSS EDR spectra (two levels) – lots of effort now vs. later Morphology from SDSS images (two levels) Bruzual & Charlot ISB modeling Quasar measurements, derived properties Compiling statistics, correlation analyses (lots of effort later vs. now) Oversight, science, figures/tables, etc. Will require individual meetings – schedule ASAP
4	Friedman World Models Einstein’s Field Equations Under ideas discussed previously (cosmological principle, Weyl’s postulate, isotropy, homogeneity) the field equations reduce to the simple pair of independent equations: R is the scale factor, ρ is total inertial mass density of matter & radiation, p the associated pressure. Script R is the radius of curvature, and there’s lambda.
5	The Standard Dust Models (Λ=0) Observed Properties of Standard Objects in the Friedman World Models with zero cosmological constant (cf. Hogg 2000, chapter 5, Ned Wright’s calculator). Angular Diameters (need Angular Distance f(z)) Flux Densities (need luminosity distance f(z)) Comoving volume within redshift z In particular covered in more detail in section 7.2.8
6	The Standard Dust Models (Λ=0)
7	The Standard Dust Models (Λ=0)
8	Models for which Λ is not 0 Einstein originally used lambda to create a static (non-expanding, non-contracting) universe according to his preconceptions. Such models also popular in 1930s when the Hubble constant was thought to be 500 km/s/Mpc, creating problems with the age of the universe (less than age of Earth). Supernova results, WMAP results, both favor non-zero cosmological constant.
9	Models for which Λ is not 0 Einstein field equations become Eq. 7.56 indicates even in an empty universe there is a net force on a test particle (+ or -).
10	Models for which Λ is not 0 For those interested, there is an interpretation of scalar Higgs fields under quantum field theory (see Zeldovich 1986). Zero point vacuum fluctations associated with zero point energies of quantum fields results in a negative energy equation of state (having “tension” rather than “pressure”). Quantum field theory can then make predictions about the value of a cosmological constant – and is off by some 120 orders of magnitude! Works for inflationary period, but not now.
11	Models for which Λ is not 0 Can rewrite field equations in terms of mass-energy densities:
12	Models for which Λ is not 0 Can then identify lambda with vacuum mass density: So now can interpret lambda in terms of “omega – lambda” which is often used in discussions. What of q, the deceleration parameter, in these models?
13	Models for which Λ is not 0 Equations 7.60 and 7.62 now give us: And can rewrite the dynamical equations (again!)
14	Models for which Λ is not 0 Substituting the values of R, dR/dt, and R = 1 at the present epoch, we can solve for curvature of space given the contributions to Omega:
15	Dynamics of Models with Λ not 0 If Lambda < 0, Omega_Lambda is less than zero, and the term will enhance gravity. In all cases expansion is eventually reversed. Models with Lambda > 0, we essentially incorporate a repulsive force that opposes gravity. Some of the mathematical details in the text.
16	Dynamics of Models with Λ not 0
17	Dynamics of Models with Λ not 0
18	Dynamics of Models with Λ not 0
19	Dynamics of Models with Λ not 0
20	Dynamics of Models with Λ not 0
21	Inhomogeneous World Models
22	Inhomogeneous World Models Because the real world is not perfectly homogeneous, is it? These perturbations cause deviations of the paths of light rays and must be taken into account for some applications.
23	Inhomogeneous World Models How one observable changes with homogeneity. Lensing effects are also a result of inhomogeneities.