This talk will focus mostly on recent efforts to determine the cosmological parameters:

New Observational Tools:

Keck Twin 10-meter telescopes
Spectroscopy of very Distant Galaxies

A Cosmological Observatory

Morphology of Distant Galaxies
Building Blocks?

Individual Cepheids in Virgo

Theoretical Framework

We have to create a framework in which we can relate observationally determined parameters to the large scale characteristics of the Universe:

We assume the Universe to be isotropic and homogeneous. In this situation the length of a Geodesic is described by the Robertson-Walker metric:

Where

• R(t) is the Universal Scale Factor that describes the expansion as a function of time
• k is a constant (-1,0,+1) that specifies the geometry (curvature) of the surface
• r is the co-moving coordinate
• Gravity enters the RW metric through R(t) and k

The gravitational acceleration of the Universe is given by Poisson's Equation:

In the early Universe, pressure from the photon field was very high and the universe acts as an isotropic fluid. Thus Poisson's equation is modified to

The effective gravitational mass density has been increased due to the photon pressure. This gravitational mass density acts to retard the expansion.

Consider an expanding spherical region with radius r_s which has some net gravitational acceleration.

Solve for p:

Now let's assume the universe is static: all derivatives with respect to r_s disappear and we have

Since mass (r) is positive:

This last equation shows that the rate of change of R(t) (e.g. the expansion rate H_o) depends on

• the density (W)which determines the net gravitational acceleration
• the curvature of the Universe
• the vacuum energy term (L)which acts as a long range repulsive force

Observers seek to measure H_o,W, L cosmology is specified.

Notes:

For K = L = 0 have:

H_o² = (8p/3)Gr H_o^-1 is a dynamical timescale.

Measuring H_o from V_r= H_od how hard can that be?

The Extragalactic Distance Scale Ladder:

Log Parsecs

HST allows for direct detection of Cepheid Variables in individual galaxies in the Virgo cluster Key Project.

However, one must know the distance to the LMC accurately to derive and accurate value for H_o from the distance and cosmic velocity of Virgo.

To get beyond Virgo requires the Tully-Fisher relation as calibrated via the Cepheids.

Results to date: H_o 70 -- 90 km/s Mpc^-1 expansion age 11.1 -- 14.2 Gyrs

Reasonable agreement with the ages of the oldest stars found in Globular Clusters

Some other methods give H_o 50 -70 km/s Mpc^-1

Sunyaev-Zeldovich effect complicated. Frequency shift of CMB photons due to Compton scattering by free electrons in an ionized cluster. Xray flux depends on n_e², D T depends only on n_e can get distance but there are several complicating factors.

Timing delays due to Gravitational lensing.

Supernova as Standard Candles. The idea here is that Supernova achieve a standard luminosity at a specified time in their light curve.

Recent Results on the Determination of H_o

Okay, What about W:

Determine W four ways:

Using some standard candle measure the change of slope in the Hubble Diagram with redshift Prone to evolutionary systematics (often ignored)

Using dynamical methods by measuring deviations from expansion motion near regions of local overdensity (e.g. galaxy clusters)

Fitting the Power Spectrum of the Galaxy distribution. Standard CDM (W = 1) either fails to reproduce the observed power on large scales, or predicts too much power on small scales. Low W models fit the data best.

Baryon Mass fractions: W_b = f*W

W_b comes from nucleosynthesis constraints which are reasonably tight. W_b~ 0.02--0.04.

f comes from some astrophysical laboratory cluster of galaxies. If f is high and W =1 then the nucleosynthesis constraint is strongly violated. Analysis of clusters of galaxies (including the hot gas) yields f ~ 0.2 - 0.3 W ~ 0.1 -- 0.2.

The above methods all argue for W < 0.3 There is no evidence for W =1.0.

Moreover,

Too massive of clusters now exist

These observations, along with the fact that these luminosities and temperatures of the high-z clusters all agree with the low-z LX-TX relation, argue strongly that Omega 0 < 1. Otherwise, the initial perturbations must be non-Gaussian, if these clusters' temperatures do indeed reflect their gravitational potentials.

What about L

Effect of L is to provide more volume per unit redshift interval effects Hubble diagram; increases the number of distant sources of any kind (quasars, gravitational lenses, etc).

Back to Supernova:

Shows that W < 1 but not much constraint on L

Other Evidence for Non-Zero L:

1. If globular clusters are 16 billion years old (or older); L > 0.76 so that H_ot_o > 1
   

2. Violation of age-redshift relation by old galaxies at high redshift.

3. The fits to the power spectrum as well as dynamical evidence favors W ~ 0.2--0.3 Inflation wants W + L =1.

4. Standard CDM can not put enough power on small scales sufficiently fast to account for the observations of forming elliptical galaxies at z ~5. More time is required, hence non-zero L.

5. Structure of X-ray clusters as a function of redshift also suggests a greater formation time that is allowed unless L > 0 (actually > 0.76).

6. Very recent measurement of gravitational lens space density gives L = 0.7 +/- 0.1 still subject to systematics and is likely an interesting but not very credible result at the moment.

Summary remark:

Cosmology in the late 90's is substantially different than it was a mere 10 years ago. Hopefully the same rate of progress will be seen in the next 10 years.

How long will we continue to insist on Dark Matter despite its continued direct non-detection?