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The sensitivity of the solar g-mode oscillation spectrum to variability in the universal gravitational constant G is described. Solar models in varying G cosmologies were constructed by evolving a zero-age main-sequence stellar model to the Sun's current age, while allowing the value of G to change according to the power law G(t) proportional to t(exp -beta), where Beta approximately equals delta G/GH and H is the Hubble constant. All solar models were constrained to the observed luminosity and radius at the current age of the Sun by adjusting the helium abundance and the mixing-length parameter of the models in the usual way for standard stellar models. Low-l g-mode oscillation periods were calculated for each of the models and compared to the claimed observation of the solar g-mode oscillation spectrum by Hill & Gu (1990). If one accepts Hill & Gu's claims, then within the uncertainties of the physics of the solar model calculation, our models rule out all but (delta G/GH) less than approximately 0.05. In other words, we conclude that G could not have varied by more than 2% over the past 4.5 Gyr, the lifetime of the present-day Sun. This result lends independent support to the validity of the standard solar model.

In order to explore the ability of helioseismology and features of solar models to test the constancy of the gravitational constant G during the last 4.5 Gyr of solar evolution, we have constructed a grid of evolutionary sequences for solar models under the assumptions that G varies with time, and have explored the sensitivity of their nonradial acoustic mode oscillation spectra to G variability. All final models satisfy the standard constraints for the present Sun and, except for the variation in G, were constructed under the assumptions of a standard solar model. When compared with the observed solar p-mode spectrum, our models definitely rule out beta greater than 0.4 and beta less than -0.4, where G(t) proportional to t(exp -beta) over the last 4.5 Gyr. These limits can be tightened to rule out absolute value of beta greater than 0 (0.1) by the use of other solar observables. For nonmonotonic variation in G this suggests that long-timescale variations greater than 0 (5%) in G are ruled out over the last 4.5 Gyr. Future prospects for improving the sensitivity of helioseismic tests of a varying G are also discussed. Finally, we explore the sensitivity of the predicted solar neutrino flux to varying G.

The lensing effect of curved space, which can cause the angular diameter of a fixed reference length seen on the sky to reach a minimum and then increase with redshift, has recently been claimed to provide evidence, using compact radio sources, for a q sub 0 = 1/2 expansion. We show here that this relation, in particular the position of the observed minimum, depends sensitively on the value of the cosmological constant, Lambda, in a flat universe. The sensitivity to a nonzero Lambda in a flat universe is compared to the sensitivity to q sub 0 in an open universe without a cosmological constant. The reported results could provide the strongest available limit on the cosmological constant in a flat universe (and on Omega in an open universe) and so we explore how uncertainties in distance measures and evolution of the sources can affect the results. Evolution of less than 30 percent in source size for z of less than 2 can completely alter the results, and so must be convincingly ruled out if this technique is to provide a new tool for cosmology.