Stochastic Inflation in Compact Extra Dimensions

While moving down the potential on its classical slow roll trajectory, the inflaton field is subject to quantum jumps, which take it up or down the potential at random. In "stochastic inflation", the impact of these quantum jumps is modeled by smoothing out the field over (at least) Hubble-patch sized domains and treating fluctuations on smaller scales as noise. The inflaton thus becomes a stochastic process whose values at a given time are calculated using its probability distribution. We generalize this approach for non-canonic kinetic terms of Dirac Born Infeld (DBI) type and investigate the resulting modifications of the field's trajectory. Since models of DBI inflation arise from string-inspired scenarios in which the scalar field has a geometric interpretation, we insist that field value restrictions imposed by the model's string origin must be respected at the quantum level.Comment: Proceedings of the ERE 2010 conference, 4 pages, 1 figur

Supersymmetry Changing Bubbles in String Theory

We give examples of string compactifications to 4d Minkowski space with different amounts of supersymmetry that can be connected by spherical domain walls. The tension of these domain walls is tunably lower than the 4d Planck scale. The ``stringy'' description of these walls is known in terms of certain configurations of wrapped Dirichlet and NS branes. This construction allows us to connect a variety of vacua with 4d N=4,3,2,1 supersymmetry.Comment: 11 pages, harvmac, no figures, reference added, minor correction

Relaxing to Three Dimensions

We propose a new selection principle for distinguishing among possible vacua that we call the "relaxation principle". The idea is that the universe will naturally select among possible vacua through its cosmological evolution, and the configuration with the biggest filling fraction is the likeliest. We apply this idea to the question of the number of dimensions of space. We show that under conventional (but higher-dimensional) FRW evolution, a universe filled with equal numbers of branes and antibranes will naturally come to be dominated by 3-branes and 7-branes. We show why this might help explain the number of dimensions that are experienced in our visible universe.Comment: 4 pages; minor improvements, references adde

A Self-Tuning Solution of the Cosmological Constant Problem

We discuss the four-dimensional cosmological constant problem in a five-dimensional setting. A scalar field coupled to the SM forms dynamically a smooth brane with four-dimensional Poincare invariance, independently of SM physics. In this respect, our solution may be regarded as a self-tuning solution, free of any singularities and fine-tuning problems.Comment: latex, 4 pages, some new material adde

The Scaling of the No Scale Potential and de Sitter Model Building

We propose a variant of the KKLT (A)dS flux vacuum construction which does not require an antibrane to source the volume modulus. The strategy is to find nonzero local minima of the no-scale potential in the complex structure and dilaton directions in moduli space. The corresponding no-scale potential expanded about this point sources the volume modulus in the same way as does the antibrane of the KKLT construction. We exhibit explicit examples of such nonzero local minima of the no-scale potential in a simple toroidal orientifold model.Comment: 11 pages, harvmac big. v2: trivial typos fixe

Gravitational backreaction of anti-D branes in the warped compactification

We derive a low-energy effective theory for gravity with anti-D branes, which are essential to get de Sitter solutions in the type IIB string warped compactification, by taking account of gravitational backreactions of anti-D branes. In order to see the effects of the self-gravity of anti-D branes, a simplified model is studied where a 5-dimensional anti-de Sitter ({\it AdS}) spacetime is realized by the bulk cosmological constant and the 5-form flux, and anti-D branes are coupled to the 5-form field by Chern-Simon terms. The {\it AdS} spacetime is truncated by introducing UV and IR cut-off branes like the Randall-Sundrum model. We derive an effective theory for gravity on the UV brane and reproduce the familiar result that the tensions of the anti-D branes give potentials suppressed by the forth-power of the warp factor at the location of the anti-D branes. However, in this simplified model, the potential energy never inflates the UV brane, although the anti-D-branes are inflating. The UV brane is dominated by dark radiation coming from the projection of the 5-dimensional Weyl tensor, unless the moduli fields for the anti-D branes are stabilized. We comment on the possibility of avoiding this problem in a realistic string theory compactification.Comment: typos corrected, 11 pages, 3 figure

Volume Stabilization and the Origin of the Inflaton Shift Symmetry in String Theory

The main problem of inflation in string theory is finding the models with a flat potential, consistent with stabilization of the volume of the compactified space. This can be achieved in the theories where the potential has (an approximate) shift symmetry in the inflaton direction. We will identify a class of models where the shift symmetry uniquely follows from the underlying mathematical structure of the theory. It is related to the symmetry properties of the corresponding coset space and the period matrix of special geometry, which shows how the gauge coupling depends on the volume and the position of the branes. In particular, for type IIB string theory on K3xT^2/Z with D3 or D7 moduli belonging to vector multiplets, the shift symmetry is a part of SO(2,2+n) symmetry of the coset space [SU(1,1)/ U(1)]x[SO(2,2+n)/(SO(2)x SO(2+n)]. The absence of a prepotential, specific for the stringy version of supergravity, plays a prominent role in this construction, which may provide a viable mechanism for the accelerated expansion and inflation in the early universe.Comment: 12 page

Lectures on Warped Compactifications and Stringy Brane Constructions

In these lectures, two different aspects of brane world scenarios in 5d gravity or string theory are discussed. In the first two lectures, work on how warped compactifications of 5d gravity theories can change the guise of the hierarchy problem and the cosmological constant problem is reviewed, and a discussion of several issues which remain unclear in this context is provided. In the next two lectures, microscopic constructions in string theory which involve D-branes wrapped on cycles of Calabi-Yau manifolds are described. The focus is on computing the superpotential in the brane worldvolume field theory. Such calculations may be a necessary step towards understanding e.g. supersymmetry breaking and moduli stabilization in stringy realizations of such scenarios, and are of intrinsic interest as probes of the quantum geometry of the Calabi-Yau space.Comment: 31 pages, harvmac big. To appear in the proceedings of TASI 1999 and the 2000 Trieste Spring Workshop on Superstring