To re-examine the rich cluster $\Omega$ value the CNOC Cluster Survey has observed 16 high X-ray luminosity clusters in the redshift range 0.17 to 0.55, obtaining approximately 2600 velocities in their fields. Directly adding all the K and evolution corrected $r$ band light to $M_r(0)=-18.5$, about $0.2L_\ast$, and correcting for the light below the limit, the average mass-to-light ratio of the clusters is $283\pm27h\msun/\lsun$ and the average mass per galaxy is $3.5\pm0.4\times10^{12}h^{-1}\msun$. The clusters are consistent with having a universal $M_v/L$ value (within the errors of about 20\%) independent of their velocity dispersion, mean color of their galaxies, blue galaxy content, redshift, or mean interior density. Using field galaxies within the same data set, with the same corrections, we find that the closure mass-to-light, $\rho_c/j$, is $1160\pm130h\msun/\lsun$ and the closure mass per galaxy, $\rho_c/\phi(>0.2L_\ast)$, is $13.2\pm1.9\times10^{12}h^{-1}\msun$. Under the assumptions that the galaxies are distributed like the mass and that the galaxy luminosities and numbers are statistically conserved, which these data indirectly support, $\Omega_0=0.20\pm0.04\pm0.09$ where the errors are, respectively, the $1\sigma$ internal and an estimate of the $1\sigma$ systematic error resulting from the luminosity normalization.

Galaxy Cluster Virial Masses and Omega

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others

https://link.springer.com/content/pdf/10.12942%2Flrr-2004-9.pdf

Gravitational Lensing from a Spacetime Perspective

http://diposit.ub.edu/dspace/bitstream/2445/119262/1/670717.pdf

Beyond ΛCDM: Problems, solutions, and the road ahead

Relativistic Cosmology: The standard model and extensions

Despite its continued observational successes, there is a persistent (and growing) interest in extending cosmology beyond the standard model, $\Lambda$CDM. This is motivated by a range of apparently serious theoretical issues, involving such questions as the cosmological constant problem, the particle nature of dark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and on small scales, and the predictivity and testability of the inflationary paradigm. In this paper, we summarize the current status of $\Lambda$CDM as a physical theory, and review investigations into possible alternatives along a number of different lines, with a particular focus on highlighting the most promising directions. While the fundamental problems are proving reluctant to yield, the study of alternative cosmologies has led to considerable progress, with much more to come if hopes about forthcoming high-precision observations and new theoretical ideas are fulfilled.

Beyond $\Lambda$CDM: Problems, solutions, and the road ahead

Ideal observational cosmology

The authors give the exact spherically symmetric solution of the Einstein field equations for dust (p=0) in observational coordinates for data on the past light cone C-(p0) consisting of redshifts, observer area distances, and galaxy number counts. A Bondi potential is found, which facilitates the integration. Also they show in detail how FLRW models can be constructed via these solutions from FLRW data. Finally, they discuss their approach with respect to other observationally oriented treatments, particularly those of Ehlers and Rindler (1987), and Rindler and Suson (1989).

S.D. Nel

Papers

Ideal observational cosmology

Observational cosmology. III. Exact spherically symmetric dust solutions