The nature of the dark energy that dominates the universe is unknown, and it is likely that a unified theory of quantum mechanics and gravity is needed to reveal its secrets. String theory has been claimed to provide a solution to the problem through its support of the idea of a multiverse. It is suggested that string theory can give rise to a huge number of different universes with varying properties – including the amount of dark energy.
In my recent research I have argued that the difficulties in stringy model building have been underestimated, and that our understanding of an eventual multiverse is rudimentary. Results of my research suggest that string cosmologies with dark energy could be less common and more fragile than anticipated. It is important to expose the assumptions and shortcomings of current constructions, develop new tools to address the problem of dark energy, construct alternative models, and establish rigorous results.
The problem of dark energy and accelerated expansion may also have profound implications for quantum gravity and the physics of black holes. This is also something that I work on.
There are a couple of posts in English on my blog where I discuss related subjects. One about a new proposal for what a black hole really is, and one on the recent crisis in string theory, where my own work has played an important role. This piece by Scientific American provides a popular account of what is going on.
You can find a list of my papers here.