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Zeta-function regularization is applied to evaluate the one-loop effectivepotential for SO(10) grand-unified theories in de Sitter cosmologies. When theHiggs scalar field belongs to the 210-dimensional irreducible representation ofSO(10), attention is focused on the mass matrix relevant for theSU(3)xSU(2)xU(1) symmetry-breaking direction, to agree with low-energyphenomenology of the particle-physics standard model. The analysis isrestricted to those values of the tree-level-potential parameters for which theabsolute minima of the classical potential have been evaluated. As shown in therecent literature, such minima turn out to be SO(6)xSO(4)- orSU(3)xSU(2)xSU(2)xU(1)-invariant. Electroweak phenomenology is more naturallyderived, however, from the former minima. Hence the values of the parametersleading to the alternative set of minima have been discarded. Within thisframework, flat-space limit and general form of the one-loop effectivepotential are studied in detail by using analytic and numerical methods. Itturns out that, as far as the absolute-minimum direction is concerned, theflat-space limit of the one-loop calculation about a de Sitter background doesnot change the results previously obtained in the literature, where thetree-level potential in flat space-time was studied. Moreover, when curvatureeffects are no longer negligible in the one-loop potential, it is found thatthe early universe remains bound to reach only the SO(6)xSO(4) absoluteminimum.Comment: 25 pages, plain Tex, plus Latex file of the tables appended at the  end. Published in Classical and Quantum Gravity, Vol. 11, pp. 2031-2044,  August 199

One-loop effective potential for SO(10) GUT theories in de Sitter space