Orientifolds with three-form flux provide some of the simplest string examples of warped compactification. In this paper we show that some models of this type have the unusual feature of D = 4, N = 3 spacetime supersymmetry. We discuss their construction and low energy physics. Although the local form of the moduli space is fully determined by supersymmetry, to find its global form requires a careful study of the BPS spectrum.

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 consider inflationary cosmology in the context of string compactifications with multiple throats. In scenarios where the warping differs significantly between throats, string and Kaluza-Klein physics can generate potentially observable corrections to the cosmology of inflation and reheating. First we demonstrate that a very low string scale in the ground state compactification is incompatible with a high Hubble scale during inflation, and we propose that the compactification geometry is altered during inflation. In this configuration, the lowest scale is just above the Hubble scale, which is compatible with the effective field theory but still leads to potentially observable cosmic microwave background corrections. Also in the appropriate region of parameter space, we find that reheating leads to a phase of long open strings in the standard model sector (before the usual radiation-dominated phase). We sketch the cosmology of the long string phase and we discuss possible observational consequences.

We study string interaction rates in the Brandenberger-Vafa scenario, the very early universe cosmology of a gas of strings. This cosmology starts with the assumption that all spatial dimensions are compact and initially have string scale radii; some dimensions grow due to some thermal or quantum fluctuation which acts as an initial expansion velocity. Based on simple arguments from the low energy equations of motion and string thermodynamics, we demonstrate that the interaction rates of strings are negligible, so the common assumption of thermal equilibrium cannot apply. We also present a new analysis of the cosmological evolution of strings on compact manifolds of large radius. Then we discuss modifications that should be considered to the usual Brandenberger-Vafa scenario. To confirm our simple arguments, we give a numerical calculation of the annihilation rate of winding strings. In calculating the rate, we also show that the quantum mechanics of strings in small spaces is important.

Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a tendimensional approach to find a new class of four-dimensional supersymmetric AdS 4 compactifications on almost-Hermitian manifolds of SU3 structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly Kähler. We argue that all moduli are fixed, and we show that the Kähler potential and superpotential proposed in the literature yield the correct AdS 4 radius. In the nearly Kähler case, we are able to solve the H Bianchi identity using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate.