We say that a de Sitter space-time is unstable if one or more of the scalar masses is negative. So for a number of unstable de Sitter vacua have been constructed but there are no examples of a stable de Sitter vacuum. In my research I try to find a specific scalar that always has a negative mass when the scalar potential is positive. Finding such a scalar would prove that there are no stable de Sitter vacuum in maximal supergravity.
(Half-)maximal supergravities appear as low energy effective descriptions of string theory compactifications. The embedding tensor formalism uses the global symmetry group of such theories as a guideline to comprise all the consistent gaugings in a single, universal and duality-covariant formulation. Nevertheless, not all these gaugings have a clear higher-dimensional origin in terms of a string compactification. It is exactly based on duality-covariance that non-geometric fluxes were first introduced. Double Field Theory has been recently developed in order to implement T-duality symmetries at a more fundamental level. Such a duality interchanges momentum and winding modes related to every compact spacetime direction, making non-geometric fluxes appear as normal twists on a doubled space were both ordinary and winding coordinates are present. Our aim is that of classifying the most-general gaugings of (half-)maximal supergravities in terms of duality orbits and, for those orbits not containing any geometric background as representative, finding yet a double field theory construction giving rise to them.
It is of great interest to understand the possibility to realise stable De Sitter and/or inflation in string theory or its effective supergravity description. Over the last year a powerful new technique has been put forward to analyse this in specific cases. It singles out the direction in moduli space associated with supersymmetry breaking. This technique has been used to rule out stable De Sitter in a variety of N = 1 and N = 2 theories, with analogous implications for slow-roll inflation. We are interested in similar aspects of a number of other cases.
Ordinary (e.g. Calabi-Yau) compactifications lead to a wide number of massless scalars, the so-called moduli. These are problematic for a number of phenomenological reasons (fifth forces, decompactification, overclosing the Universe, spoiling BBN etc). One way to introduce masses for these scalar fields is by turning on fluxes in the compactification manifold. In addition to gauge and geometric fluxes, it has been argued on duality grounds that string theory also makes sense with non-geometric fluxes. Such backgrounds consist of different patches that are glued together with a transition function that includes e.g. a T-duality transformation. One point of interest ishow non-geometric fluxes appear in the effective four-dimensional description and whether they allow for De Sitter in an context.
Supergravities with supersymmetries appear as an effective, four-dimensional descriptions of a class of string compactifications. Their dynamics is very much constrained by the large amount of supersymmetry. This allows for a clear analysis of the issue of moduli stabilisation. In particular, in order to achieve this, the theory needs to possess a particular property, called non-trivial duality angles. First introduced in 1985 in supergravity, the string theory origin of these angles was unclear. Recently, an understanding of how these can be generated in orientifold reductions has emerged. One of our aims is to extend these reductions to obtain more general gaugings and more interesting vacua.
An additional point of interest are the De Sitter solutions in theories. In contrast to the known examples, these are actually stable solutions. It has always been a bit of a mystery as to what makes these solutions tick. Very recently, we have uncovered a web of relations between supergravity models with De Sitter solutions and different amounts of supersymmetry. In particular, this explains how the models follow by a simple supersymmetry truncation from the much better understood models. In addition to the known examples this gives rise to new models with stable De Sitter vacua. In the future we aim to investigate a number of aspects concerning their relation to string theory.
In Anti-de Sitter space-time there is the famous Breitenlohner-Freedman bound, stating that scalar fields with negative mass are not tachyonic in a certain range of the mass parameter. Is there an analogous bound for fields in De Sitter space-time? More generally, how can one define a mass in De Sitter space-time? And can one understand this from gauge invariance and/or representation theory, and what's the relation between these two? Another question would be what the representations of the fields of supergravity in a De Sitter vacuum are.
In addition to these points we have a wide range of other topics for e.g. a Bachelor's or Master's research project. Just to mention a few, examples would be e.g. investigating whether the Higgs scalar field could act as the inflaton after all, or how string gas cosmology might answer the question why we live in 3+1 dimensions.