Kaluza-Klein theory for type $IIb$ supergravity on the warped deformed conifold

We discuss Kaluza-Klein theory for type $IIb$ supergravity on the warped deformed conifold using a large radial distance limit of Klebanov-Strassler solution where the radial coordinate separates from angle coordinates for a background asymptotic to $Ad{S}_5\times T^{1,1}$ spacetime. The decomposition of field fluctuations on harmonics of the base manifold $T^{1,1}$ and plane waves of $M_4=\mathrm{ð}(Ad{S}_5)$ is examined for the metric tensor components along $M_4=\mathrm{ð}(Ad{S}_5)$, the axio-dilaton and the 4-form potential components along $T^{1,1}$. Semi-classical methods are used to compute the mass spectra, wave functions and interactions for a set of modes in low dimensional representations of the isometry group. Deformations of the background solution due to compactification effects are also considered. The information on warped modes properties is utilized to explore the thermal evolution of a cosmic component of metastable modes after exit from brane inflation.