We develop a model of eternal topological inflation using a racetrack potential within the context of type IIB string theory with KKLT volume stabilization. The inflaton field is the imaginary part of the Kähler structure modulus, which is an axion-like field in the 4D effective field theory. This model does not require moving branes, and in this sense it is simpler than other models of string theory inflation. Contrary to single-exponential models, the structure of the potential in this example allows for the existence of saddle points between two degenerate local minima for which the slow-roll conditions can be satisfied in a particular range of parameter space. We conjecture that this type of inflation should be present in more general realizations of the modular landscape. We also consider 'irrational' models having a dense set of minima, and discuss their possible relevance for the cosmological constant problem.

We perform a general study about the existence of non-supersymmetric minima with vanishing cosmological constant in supergravity models involving only chiral superfields. We study the conditions under which the matrix of second derivatives of the scalar potential is positive definite. We show that there exist very simple and strong necessary conditions for stability that constrain the Kähler curvature and the ratios of the supersymmetry-breaking auxiliary fields defining the Goldstino direction. We then derive more explicitly the implications of these constraints in the case where the Kähler potential for the supersymmetry-breaking fields is separable into a sum of terms for each of the fields. We also discuss the implications of our general results on the dynamics of moduli fields arising in string compactifications and on the relative sizes of their auxiliary fields, which are relevant for the soft terms of matter fields. We finally comment on how the idea of uplifting a supersymmetric AdS vacuum fits into our general study.

We present a new version of our racetrack inflation scenario which, unlike our original proposal, is based on an explicit compactification of type IIB string theory: the Calabi-Yau manifold IP 4 [1,1,1,6,9] . The axion-dilaton and all complex structure moduli are stabilized by fluxes. The remaining 2 Kähler moduli are stabilized by a nonperturbative superpotential, which has been explicitly computed. For this model we identify situations for which a linear combination of the axionic parts of the two Kähler moduli acts as an inflaton. As in our previous scenario, inflation begins at a saddle point of the scalar potential and proceeds as an eternal topological inflation. For a certain range of inflationary parameters, we obtain the COBEnormalized spectrum of metric perturbations and an inflationary scale of M = 3 × 10 14 GeV. We discuss possible changes of parameters of our model and argue that anthropic considerations favor those parameters that lead to a nearly flat spectrum of inflationary perturbations, which in our case is characterized by the spectral index n s = 0.95.

We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N = 1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kähler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the 'sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kähler potential which break the no-scale property may allow to lift these masses.

We further develop on the study of the conditions for the existence of locally stable non-supersymmetric vacua with vanishing cosmological constant in supergravity models involving only chiral superfields. Starting from the two necessary conditions for flatness and stability derived in a previous paper (which involve the Kähler metric and its Riemann tensor contracted with the supersymmetry breaking auxiliary fields) we show that the implications of these constraints can be worked out exactly not only for factorizable scalar manifolds, but also for symmetric coset manifolds. In both cases, the conditions imply a strong restriction on the Kähler geometry and constrain the vector of auxiliary fields defining the Goldstino direction to lie in a certain cone. We then apply these results to the various homogeneous coset manifolds spanned by the moduli and untwisted matter fields arising in string compactifications, and discuss their implications. Finally, we also discuss what can be said for completely arbitrary scalar manifolds, and derive in this more general case some explicit but weaker restrictions on the Kähler geometry.