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We consider a class of grand unified theories (GUT's) based on the Georgi-Glashow model in curved spacetime. We are particularly concerned with the coupling constants involving the curvature. These include the cosmological and gravitational constants, as well as coupling constants appearing in terms quadratic in the curvature and in terms which link the Higgs bosons to the scalar curvature. For asymptotically free theories, we use the renormalization group to obtain expressions for these effective coupling constants at high curvature (between the GUT and Planck scales). We discuss the role of the effective coupling constants in the gravitational field equations. These results may be of importance for cosmology.
Parker et al. (Sun,) studied this question.