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We discuss the IAU resolutions B1.3, B1.4, B1.5, and B1.9 that were adopted during the 24th General Assembly in Manchester, 2000, and provides details on and explanations for these resolutions. It is explained why they present significant progress over the corresponding IAU 1991 resolutions and why they are necessary in the light of present accuracies in astrometry, celestial mechanics, and metrology. In fact, most of these resolutions are consistent with astronomical models and software already in use. The metric tensors and gravitational potentials of both the Barycentric Celestial Reference System and the Geocentric Celestial Reference System are defined and discussed. The necessity and relevance of the two celestial reference systems are explained. The transformations of coordinates and gravitational potentials are discussed. Potential coefficients parameterizing the post-Newtonian gravitational potentials are expounded. Simplified versions of the time transformations suitable for modern clock accuracies are elucidated. Various approximations used in the resolutions are explicated and justified. Some models (e.g., for higher spin moments) that serve the purpose of estimating orders of magnitude have actually never been published before.

Cosmological models within general tensor-multiscalar theories of gravity are studied. By isolating an autonomous evolution equation for the scalar fields, one shows that the expansion of the Universe during the matter-dominated era tends to drive the scalar fields toward a minimum of the function a(rp) describing their coupling to matter, i.e. , toward a state where the tensor-scalar theory becomes indistinguishable from general relativity. The two main parameters determining the e%ciency of this natural attractor mechanism toward general relativity are the redshift at the beginning of the matter era (or equivalently the present cosmological matter density) and the curvature of the coupling function a(p). Quantitative estimates for the present level of deviation from general relativity, as measured by the post-Newtonian parameters p -1, P -1, and G/G, are derived, which give greater significance to future improvements of solar-system gravitational tests. Another prediction of many tensor-scalar scenarios (whose consequences, particularly for the formation of structure in the Universe, remain to be studied in detail) is the existence of strong oscillations of the effective Newtonian coupling strength during the first few Hubble time scales of the matter era. PACS number(s): 04.80.+z, 04.50.+h, 98.80.Cq, 98.80.Hw