We show that the minimal set of necessary ingredients to construct explicit, four-dimensional de Sitter solutions from IIA string theory at tree-level are O6-planes, non-zero Romans mass parameter, form fluxes, and negative internal curvature. To illustrate our general results, we construct such minimal simple de Sitter solutions from an orientifold compactification of compact hyperbolic spaces. In this case there are only two moduli and we demonstrate that they are stabilized to a sufficiently weakly coupled and large volume regime. We also discuss generalizations of the scenario to more general metric flux constructions.

We construct the effective theory of the universal Kähler modulus in warped compactifications using the Hamiltonian formulation of general relativity. The spacetime dependent 10d solution is constructed at the linear level for both the volume modulus and its axionic partner, and nontrivial cancellations of warping effects are found in the dimensional reduction. Our main result is that the Kähler potential is not corrected by warping, up to an overall shift in the background value of the volume modulus. We extend the analysis beyond the linearized approximation by computing the fully backreacted 10d metric corresponding to a finite volume modulus fluctuation. Also, we discuss the behavior of the modulus in strongly warped regions and show that there are no mixings with light Kaluza-Klein modes. These results are important for the phenomenology and cosmology of flux compactifications.

We discuss the four dimensional effective action for type IIB flux compactifications, and obtain the quadratic terms taking warp effects into account. The analysis includes both the 4-d zero modes and their KK excitations, which become light at large warping. We identify an 'axial' type gauge for the supergravity fluctuations, which makes the four dimensional degrees of freedom manifest. The other key ingredient is the existence of constraints coming from the ten dimensional equations of motion. Applying these conditions leads to considerable simplifications, enabling us to obtain the low energy lagrangian explicitly. In particular, the warped Kähler potential for metric moduli is computed and it is shown that there are no mixings with the KK fluctuations and the result differs from previous proposals. The four dimensional potential contains a generalization of the Gukov-Vafa-Witten term, plus usual mass terms for KK modes.

We investigate in some quantitative details the viability of reheating in multi-throat brane inflationary scenarios by estimating and comparing the time scales for the various processes involved. We also calculate within perturbative string theory the decay rate of excited closed strings into KK modes and compare with that of their decay into gravitons; we find that in the inflationary throat the former is preferred. We also find that over a small but reasonable range of parameters of the background geometry, these KK modes will preferably tunnel to another throat (possibly containing the Standard Model) instead of decaying to gravitons due largely to their suppressed coupling to the bulk gravitons. Once tunneled, the same suppressed coupling to the gravitons again allows them to reheat the Standard Model efficiently. We also consider the effects of adding more throats to the system and find that for extra throats with small warping, reheating still seems viable.

Previous work on DBI inflation, which achieves inflation through the motion of a D3 brane as it moves through a warped throat compactification, has focused on the region far from the tip of the throat. Since reheating and other observable effects typically occur near the tip, a more detailed study of this region is required. To investigate these effects we consider a generalized warp throat where the warp factor becomes nearly constant near the tip. We find that it is possible to obtain 60 or more e-folds in the constant region, however large non-gaussianities are typically produced due to the small sound speed of fluctuations. For a particular well-studied throat, the Klebanov-Strassler solution, we find that inflation near the tip may be generic and it is difficult to satisfy current bounds on non-gaussianity, but other throat solutions may evade these difficulties. †