Update of the Main Themes

Modern Cosmological Observations and Problems

Distance Scale: RR Lyrae vs. Cepheids

Primordial Helium Abundance

Cosmological Constant

Further verification of Big Bang Model

The Distance Scale: Lingering Ambiguity

In the book we have tried to outline that there is significant disagreement between the distance to the LMC as inferred from Cepheids (m-M = 18.55 +/- 0.05 I suppose) with that inferred from RR Lyraes (m-M = 18.35 +/- 0.05). This problem has not gone away, despite some claims to the contrary with respect to recent Hipparchos re-calibration of the RR Lyrae magnitude scale. To recent references that illuminate these disagreements are:

• Caputo 1997 The period-magnitude diagram of RR Lyrae stars - I. The controversy about the distance scale (highly recommended reading)
• Freedman and Madore (1998) Hipparcos Parallaxes and the Cepheid Distance Scale

In addition to the above references, there are a couple of other noteworthy publications that remind us that we have not yet determined H_o to an unambiguous accuracy of 10%.

• Cepheid metallicity and Hubble constant (H = 68).

• An Unbiased Estimate of the Global Hubble Constant in the Region of Pisces-Perseus (H = 65).

• The Far Field Hubble constant (H = 89).

• Type I supernova and the Hubble constant (H=60).

• Determining the Hubble Constant from the Gravitational Lens PG 1115+080 (H = 51).

• A Measurement of the Hubble Constant from the X-Ray Properties and the Sunyaev-Zeldovich Effect of CL 0016+16 (H=42).

Finally, there have been two new studies which do a reasonable job in showing the presence of systematic errors in use the of the SZ effect to determine H_o. These references are:

• On the Cluster Sunyaev-Zeldovich Effect and Hubble Constant

• Systematic Errors in the Hubble Constant Based upon Measurement of the Sunyaev-Zeldovich Effect

So, it would seem that H_o is still in the likely range of 60 -90 km/s and everyone and their dog will write a paper that recovers this result.

The Primoridal Helium Abundance

In a recent paper, Olive, Skillman and Steigman (1998) have re-assessed the data concerning the primordial Helium abundance. As discussed in this book, an accurate value for this quantity, denoted by Y_p, provides a very important constraint on the baryon density via primoridal nucleosynthesis. Olive etal. summarize a variety of new observations including a) a plethora of H II region abundance measurements in very chemically unevolved galaxies and b) the recent HST observations of the Deuterium_alpha line in the spectra of distant QSOs. In this re-assessment the authors find:

• Y_p = 0.234 +/- 0.002 +/- 0.005 (systematic) This value is not significantly different from that previously measured.

• Given this value they find that W h² (Omega-h²) has an upper bound of 0.008 and could be as low as 0.005. These baryon densities are lower than the ones quoted in the book as derived by Walker etal (1991) (although they are within the errors). These lower numbers help to ease the "missing" baryon problem discussed in the book.

Measuring the CMB Temperature at z = 2

A straightforward prediction of standard big bang cosmology is that the temperature of the Universe declines linearly with redshift. Recently, Ge etal 1997 were able to measured the excited state of Carbon I within a damped lyman alpha system at z = 1.97. The measurement of the excitation temperature provides an upper limit on the CMB temperature at that redshift if one assumes that all the excitation comes from CMB photons.

Ge etal modelled the excitation that could come from other sources such as collisions and/or UV pumping (either from the metagalactic UV flux or from the distant QSO). When these other sources of excitation are taking into account, the derived CMB temperature at z = 1.97 is 7.9 +/1 1 K. Using a CMD temperature at z = 0 of 2.74 K predicts T_z=1.97 = 8.1 K, well within the error bars. This good agreement is a strong verification that the MWB we observe today is indeed relic radiation.

More Evidence for a Positive Cosmological Constant?

As the book is currently written, there are several places which suggest that certain "problems" can be resolved if the Cosmological Constant (CC) is non-zero. Various lines of evidence in support of that proposition were offered. Interestingly, shortly after the book was published, Reiss etal 1998 published their first results on high redshift supernova which seem to support the idea that the kinematics of the Universe is now driven by the CC.

The evidence comes from determining the curvature in the classical Hubble diagram which is a plot of redshift vs apparent magnitude. If there is no luminosity evolution in the source, such a diagram will reveal the deceleration parameter of the Universe, q_o. The method works as follows:

The relationship between the luminosity distance, d_L and the redshift of a galaxy, z , can be expressed as a power series where only the first two terms are important:

H_od_L = z + 0.5(1- q_o)z² + ...

In the case of q_o = 1.0, the relationship is strictly linear. Now since d_L ~ (L/F)^1/2, where L = intrinsic luminosity and F = the measured flux then if we can find a population of sources in which L is constant, we just plot measured flux, F, vs redshift and determine q_o.

While this is a classic test of cosmology (and therefore is discussed in Peebles, Weinberg, etc) it was not included in this book primarily because any astrophysical source will have luminosity evolution and hence attempts to determine q_o in this manner are subject to model dependent evolutionary corrections. Historically this was first done assuming the brightest galaxy in a cluster of galaxies had a fixed L. As more data were acquired, it became apparent that this could not be the case and the evolutionary corrections to L became difficult to accurately model. I don't consider the Hubble diagram to be a clean laboratory for measuring q_o.

From the form of equation we can see that values of q_o > 1 means that objects of a given apparent flux, will be located at a higher redshift. For values of q_o < 1, they will be located at a lower redshift. In essence, q_o is a measure of the value of the expansion parameter, H_o, at some particular redshift. If the universe is matter dominated, then H_o is being lowered as gravity slows down the expansion of the Universe. The slope of the line in the redshift-distance relationship is H_o. Thus, at some distant redshift, H_o has a higher value than it does now, and this would produce a non-constant slope (i.e. curvature) in the redshift-distance relation if it goes out to sufficiently high redshift to see the effect. If the universe is dominated by vacuum energy, then, q_o will be negative. This means the universe is accelerating and H_o is higher now than it was in the past. In this scenario, the Universe is then older than H_o^-1 as discussed in Chapter 2 and elsewhere in the book.

A schematic illustration of this is shown below.

Here we see that the various deflections away from the q_o = 1 linear relation. The deflections first become noticeable at a redshift of about 1/2 and are obvious by a redshift of 2. Of course, astrophysical sources at redshift = 2 have quite low fluxes and are difficult to measure accurately.

The Reiss etal 1998 dataset uses the Multicolor Light Curve correction scheme for Supernova to correct them to a common luminosity. This is discussed on pages 59--64. Their sample consists of 16 supernova with redshift between z = 0.16 -- 0.97. The determined distances are 10--15% farther than would be expected in a matter dominated Universe. This indicates that q_o is less than zero. Their Hubble diagram is shown below (note the Y-axis is distance modulus, m-M).

Log Redshift

The nearby and distant samples have been combined into one diagram. While formally the fit with a positive CC is better than the fit to an open Universe model (Omega_matter = 0.2), the error bars combined with the small sample size suggest that this diagram and its associated fits will evolve in the future. However, the observation that virtually all the distant Supernova sit above what would be expected for the OMEGA = 1 case, is perhaps the most significant result of this study.

The diagram above used the distance as determined by the MCLS method. Alternatively, one can use the luminosity-decline calibration of Phillips (1993) to derive the distance. The results are similar:

Log Redshift

Finally, the preferred value of the CC that results from this study leads to a dynamical age of the Universe of about 14.5 Gyr.

Summary:

While this data is encouraging, I think claims that we have observational evidence for a positive CC are premature. However, the technique is quite promising, particularly if SN can be discovered at z ~ 1. On the other hand, as pointed out by von Hippel etal (1997), there are substantial areas of concern about the calibration of intrinsic SN Ia luminosity at moderate look-back times.