The problems that are addressed concern the use of novel
symmetries, dualities and new mathematical techniques in the cosmology
of the early Universe close to the big bang. The evolution of the Universe
is very well understood in terms of accepted physical theories like
Einstein's theory of general relativity and the standard model of particle physics.
These theories tell us, with a high degree of confidence, that roughly 14 billion years ago
the Universe was in a very dense and hot state,
from which our current Universe evolved through expansion and subsequent cooling.
This is known as the big bang model. While the history of the Universe
starting very shortly after the big bang must be considered well established science,
we also know that our current physical theories break down when trying to approach
the big bang itself. More precisely, Einstein's general relativity
predicts a singularity, a state of infinite density and spacetime curvature in which the
theory itself becomes meaningless. We thus know that the Einstein's theory
can only be an approximation to a more general theory that must take over close to the
big bang (and similarly close to the center of a black hole). My research program explores
the framework of string theory in order to find such a more general theoretical description
that could be relevant close to the big bang.
Technically, there are three important respects in which any string theory introduces new
features compared to general relativity (to which it reduces in an appropriate low-energy limit):
First, it features certain so-called dualities implying that two seemingly different
solutions of the equations should actually be viewed as physically equivalent, despite
having very different properties from the viewpoint of standard geometry and physics.
The prime example is T-duality, the phenomenon that string theory on a space of size R
(like the radius of a circle) is equivalent to string theory on a space of size 1/R.
Second, string theory features so-called higher-derivative corrections. While almost all
of physics since Newton is governed by differential equations of second order, which means
that two initial conditions are needed in order to find a solution,
in string theory, at least as currently understood, there must be an infinite number of
higher-derivative corrections, controlled by a fundamental parameter of string theory,
the inverse string tension $\alpha'$.
Third, string theory features higher string modes, massive states that are not
expected to be excitable in current accelerators but which may become relevant in
the very early Universe.
The first feature, duality invariance, indeed immediately suggest promising scenarios for cosmology,
since a very small Universe could equivalently be thought of as being very large.
There have been various proposals in the string theory literature along such lines,
but unfortunately they all fall short of producing a full-fledged cosmological model with potentially
falsifiable predictions. One reason is the presence of higher-derivatives corrections and massive string modes,
whose explicit formulation is only poorly understood.
The more detailed research objectives are thus: 1) to find the higher-derivative corrections
possibly to all orders by exploiting the duality properties,
2) to write explicit field equations that govern those massive string modes that are needed
for a duality invariant formulation and 3) to apply these findings to cosmology,
for instance by determining whether massive string modes may leave imprints in the
cosmic microwave background.
This line of research is important for society because it aims to satisfy humanity's most
basic curiosity: where does the world come from? The fact that already now,
equipped with physical theories that are very well tested, we are able to go back
in time (figuratively speaking) and reconstruct the entire history of the Universe almost all the way
to the big bang is truly astonishing. There is every reason to believe that we can go even further
once we find the next theory transcending Einstein's theory.
