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Modern cosmology confronts us with several fundamental puzzles which so far have eluded satisfactory answers. These range from the initial space-like curvature singularity over the origin of cosmic inflation to puzzles at the current epoch, including most pressingly the nature of dark energy resp. dark matter and the related coincidence problem. On the observational side, the latest WMAP3 data revealed a significant red spectrum of scalar density perturbations, an indication towards a running of the spectral index and the possible presence of features in the CMB spectrum, which need to be explained.

String-theory is the prime candidate for a theory of quantum gravity. The physics of the initial singularity, at which both quantum and strong gravitational effects are important, should therefore be dictated by string-theory. Moreover, string-theory extends not only general relativity but combines it with modern particle physics, including grand unified theories. Hence, string-theory provides us with relations between gravity and gauge theories. For instance, heterotic theories predict a tight relation between Newton's constant, the GUT gauge coupling and the GUT scale. In conjunction with mechanisms for moduli stabilization, it is thus natural to consult string-theory for new insights and possible explanations of the mentioned fundamental cosmological puzzles and observations.

In fact, crucial developments in string-theory over the past decade included the introduction of D-branes, non-perturbative BFSS matrix-theory, M-theory, AdS-CFT correspondence, brane-world models, S-branes, flux compactifications, moduli stabilization, the role of open and closed string tachyons. These gave, in each case, rise to new ideas of how to approach and treat fundamental cosmology in string-theory. Among those recent advances in string cosmology are the study of time-dependent cosmological backgrounds, the role which the tachyon might have played in inflation or quintessential dark energy, or the construction of (quasi) de Sitter vacua for inflation and late-time dark energy. It culminated in several proposals of how inflation might be generated in string-theory. These comprise brane-antibrane inflation in warped backgrounds, DBI inflation in warped throats and most recently the multi-brane inflation mechanism. The latter seems to offer a natural way to avoid the supergravity eta-problem which prevents sustained inflation. The underlying theme in all three proposals are moving D-branes whose position moduli serve as inflatons. Finally, D-branes also led to viable candidates for cosmic superstrings whose detection could be the first direct observational evidence for string-theory.

Our objectives in this project are consequently broad since mathematical and physical developments in string-theory go hand in hand. The main goals are

- Construction of string models with small and positive cosmological constant, suitable for an explanation of dark energy. This requires an improved understanding of supersymmetry breaking with no or almost zero generation of vacuum energy at low energies.
- Search for stringy dark matter candidates. String-theory derivations of MSSM like models and their soft supersymmetry breaking parameters will be crucial to verify whether LSP-type particles or stringy excitations lead to realistic dark matter.
- The origin of inflation in string-theory. The initial focus will be on multi-brane inflation which, in its extension to cascade inflation, has built in D-brane mechanisms to account for features in the CMB spectrum and a possible running of the spectral index.
- A derivation of quintessence from string-theory. Non-perturbative brane-brane or brane-antibrane forces are considered for the generation of an effective quintessence potential.
- The necessary mathematical tools, foremost the relevant flux compactifications, the corresponding effective theories and related moduli stabilization mechanisms, will be developed complementary.

Contact: Dieter Lüst or
Axel Krause

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