GUT scalar potentials for Higgs inflation

Motivated by the idea that there is new physics beyond the Standard Model (SM), we have investigated a number of models for Grand Unified Theories (GUTS) in four dimensions for the possibility that their Higgs fields might be responsible for inflation in the early universe. In addition to models having an intrinsic Planck mass parameter, we have entertained classically scale invariant models in which the Planck scale itself as well as the GUT scale is induced by spontaneous breaking of the gauge symmetry. We found that in non-supersymmetric SU(5) with the usual Higgs in the adjoint representation but with large non-minimal coupling to the curvature, there appear to be several possible flat directions that might lead to inflation. Interestingly, the one of lowest energy is the breaking into SU(3) circle times SU(2) circle times U(1) that is suggested by gauge coupling unification. Further, we show that this flat direction is stable against small fluctuations in other directions. We attempted to extend this to similar supersymmetric GUTS, both global and super-gravity, but did not succeed in finding a phenomenologically acceptable model of this type, with a minimal Kahler potential augmented only by terms characterised by dimensionless coupling constants. As is often the case, such models suffered either from a negative vacuum energy or from tachyonic modes. We also considered a variant of an inverted hierarchy model in which the GUT scale is set by dimensional transmutation, but were unable to find a phenomenologically acceptable model.