Dynamics of warped compactifications and the shape of the warped landscape

The dynamics of warped/flux compactifications is studied, including warping effects, providing a firmer footing for investigation of the "landscape." We present a general formula for the four-dimensional potential of warped compactifications in terms of ten-dimensional quantities. This allows a systematic investigation of moduli-fixing effects and potentials for mobile branes. We provide a necessary criterion, "slope dominance," for evading "no-go" results for de Sitter vacua. We outline the ten-dimensional derivation of the nonperturbative effects that should accomplish this in examples of Kachru, Kallosh, Linde and Trivedi and outline a systematic discussion of their corrections. We show that potentials for mobile branes receive generic contributions inhibiting slow-roll inflation. We give a linearized analysis of general scalar perturbations of warped IIB compactifications, revealing new features for both time-independent and dependent moduli, and new aspects of the kinetic part of the four-dimensional effective action. The universal Kahler modulus is found not to be a simple scaling of the internal metric, and a prescription is given for defining holomorphic Kahler moduli, including warping effects. In the presence of mobile branes, this prescription elucidates couplings between bulk and brane fields. Our results are thus relevant to investigations of the existence of de Sitter vacua in string theory, and of their phenomenology, cosmology, and statistics.