We investigate the possibility that spiral inflation can be realized using the near-conifold flux potentials for the complex structure moduli in type IIB string theory compactified on a Calabi-Yau manifold. Using the explicit form of the flux potenti
al for complex structure moduli, we provide analytical and numerical arguments showing that spiral inflation is difficult to support. We also show that for this sector of low energy string theories, a viable spiral inflationary scenario would owe its success to a de Sitter-like vacuum energy, with minimal reliance on the non-gradient flow field trajectories which characterize spiral inflation. We thus conclude that even though the near conifold region has the requisite multi-sheeted potential called for by spiral inflation, generically it appears that spiral inflation is not realized using the complex structure flux potential alone.
We investigate flux vacua on a variety of one-parameter Calabi-Yau compactifications, and find many examples that are connected through continuous monodromy transformations. For these, we undertake a detailed analysis of the tunneling dynamics and fi
nd that tunneling trajectories typically graze the conifold point---particular 3-cycles are forced to contract during such vacuum transitions. Physically, these transitions arise from the competing effects of minimizing the energy for brane nucleation (facilitating a change in flux), versus the energy cost associated with dynamical changes in the periods of certain Calabi-Yau 3-cycles. We find that tunneling only occurs when warping due to back-reaction from the flux through the shrinking cycle is properly taken into account.
