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Spontaneously broken SU(5) symmetries and 1-loop effects in the early Universe

This paper studies the 1-loop effective potential and spontaneous-symmetry-breaking pattern for SU(5) gauge theory in de Sitter spacetime. Curvature effects modify the flat-space effective potential by means of a very complicated special function previously derived in the literature. An algebraic technique already developed by Buccella et al. to study spontaneous symmetry breaking of SU(n) for renormalizable polynomial potentials is here generalized, for SU(5), to the much more difficult case of a de Sitter background. A detailed algebraic and numerical analysis provides a better derivation of the stability of the extrema in the maximal subgroups SU(4)*U(1), SU(3)*SU(2)*U(1), SU(3)*U(1)*U(1)*R311, SU(2)*SU(2)*U(1)*U(1)+R2211, where R311 and R2211 discrete symmetries select particular directions in the corresponding two-dimensional strata. One thus obtains a deeper understanding of the result, previously found with a different numerical analysis, predicting the slide of the inflationary Universe into either the SU(3)*SU(2)*U(1) or SU(4)*U(1) extremum. Interestingly, using this approach, one can easily generalize all previous results to a more complete SU(5) tree-level potential also containing cubic terms.