Klebanov-Strassler warp-throat conifold-background will be the basis for our explicit analysis of warped D-brane inflationary cosmology

For a visual treat of the mathematical 'picture', scroll to the bottom of this post. In part two of this series on M-theoretic world-brane cosmology, I showed that a Klebanov-Strassler geometry naturally arises by considering string theory compactification on where is the Einstein manifold in five dimensions, with the interaction-Lagrangian of the massless Klebanov-Strassler field and the brane fields fermions is

then I showed that after integrating over the extra dimensional part, the effective 4-D Lagrangian reduces to

with the fundamental Planck scale and the 4-D Planck scale related as

Moreover, I demonstrated that the moduli spaces of compact Calabi-Yau spaces naturally contain conifold singularities and that the local description of these singularities is a conifold, a noncompact Calabi-Yau three-fold whose geometry is given by a cone, and that the orbifolded conifold equation

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