1	ASTR 5460, Mon. Nov. 29, 2004 Catch-up on old assignments (midterm, observing project, mini-Tac) Review new work: Last HW handed out Wed. Shorter. Proposal assignment Take-home final Final topics (mostly from Longair): Review (ch. 7-8) Thermal history of the universe (ch. 9) Synthesis of the light elements (ch. 10) Microwave background radiation -- details
2	Review Friedman World Models Einstein’s Field Equations Under ideas discussed previously (cosmological principle, isotropy, homogeneity) the field equations reduce to a 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.
3	The Standard Dust Models (Λ=0) Observed Properties of Standard Objects in the Friedman World Models with zero cosmological constant (cf. Hogg 2000, 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 Longair section 7.2.8
4	The Standard Dust Models (Λ=0)
5	The Standard Dust Models (Λ=0)
6	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.
7	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 -).
8	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.
9	Models for which Λ is not 0 Can rewrite field equations in terms of mass-energy densities:
10	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?
11	Models for which Λ is not 0 Equations 7.60 and 7.62 now give us: And can rewrite the dynamical equations (again!)
12	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:
13	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.
14	Dynamics of Models with Λ not 0
15	Dynamics of Models with Λ not 0
16	Dynamics of Models with Λ not 0
17	Dynamics of Models with Λ not 0
18	Inhomogeneous World Models
19	Thermal History of the Universe
20	Thermal History of the Universe
21	Thermal History of the Universe
22	Thermal History of the Universe
23	Thermal History of the Universe
24	Thermal History of the Universe
25	Matter/Radiation Content of the Universe
26	Matter/Radiation Content of the Universe
27	Matter/Radiation Content of the Universe
28	Matter/Radiation Content
29	Present photon-to-baryon ratio
30	Thermal History of the Universe
31	Important Epochs, Detail
32	Important Epochs, Detail
33	Important Epochs, Detail
34	Important Epochs, Detail
35	Important Epochs, Detail
36	Important Epochs, Detail
37	Important Epochs, Detail
38	Sound Speed with epoch
39	Sound Speed with epoch
40	Sound Speed with epoch
41	Early Epochs