It is established beyond doubt that nature is governed by quantum mechanics. This is well understood for all fundamental interactions, except for gravity. Despite much work over several decades, reconciling gravity with quantum mechanics remains to be one of the major open problem in theoretical physics. One of the underlying difficulties is that quantum gravity arguably entails a modification of space-time itself, which requires a broadening of the established framework to formulate physical theories. It is widely expected that space-time should have some kind of quantum structure at short distances. On the other hand, relativity requires (local) Lorentz invariance, to a very high precision. Reconciling these two requirements is a very non-trivial task.
Progress in recent years has led to the remarkable insight that space-time and geometry can emerge from simple models with little or no geometry. This happens in particular in certain matrix models models which are related to string theory, notably the so-called IKKT model. Certain solutions of this model, which were found recently, have indeed the required geometrical properties of a “quantized” cosmological space-time geometry which is exactly homogeneous and isotropic, with a discrete quantum structure at very short distances. This quantum geometry behaves as an expanding universe originating from a Big Bang, and might play the role of physical space-time.
The present project studies the physical properties of these quantized space-time solutions within the IKKT model, and in particular the gauge theory of the spin 2 modes which arise on these spaces. These naturally provide the degrees of freedom for gravity. This resulting gravity will be studied and elaborated in detail, along with its higher spin extensions, and compared with similar theories. This requires a systematic organization and analysis of all fluctuation modes on this space-time, and a description of their dynamics in the IKKT model. Other topics to be studied include quantum corrections beyond the leading classical contributions, stability issues, and properties of the Big Bang in this scenario.