Grand unification through gravitational effects

We systematically study the unification of gauge couplings in the presence of (one or more) effective dimension-5 operators cHG G =4Mpl, induced into the grand unified theory by gravitational interactions at the Planck scale. These operators alter the usual condition for gauge-coupling unification, which can, depending on the Higgs content H and vacuum expectation value, result in unification at scales MX significantly different than naively expected. We find nonsupersymmetric models of SUð5Þ and SOð10Þ unification, with natural Wilson coefficients c, that easily satisfy the constraints from proton decay. Furthermore, gauge-coupling unification at scales as high as the Planck scale seems feasible, possibly hinting at simultaneous unification of gauge and gravitational interactions. In the Appendix we work out the group theoretical aspects of this scenario for SUð5Þ and SOð10Þ unified groups in detail; this material is also relevant in the analysis of nonuniversal gaugino masses obtained from supergravity.