Concept
Solving long-standing problems is often accomplished by taking on a new viewpoint and transferring knowledge across disciplines, after standard ways of tackling the issue were explored. While mainstream science is separating in specialisation, I seek synthesis, knowledge transfer, and unification to explore such new paths together with collaborators from multiple disciplines. My research projects have greatly profited from my strong interdisciplinary background and many experiences with such collaborations.
Cosmic Trinity
In cosmology there are three branches of knowledge gain complementing each other in their goals:
In my projects, the focus lies on "Why?" and the connection of observations and simulations to the mathematical theory. Within this setting, any cosmological model based on some theory of gravity is a fit to our observations. It approximately describes the data up to our finite measurement precision and compresses the information contained in real structures into a reduced set of fundamental physical laws – the prescriptions for generating such structures. Numerical simulations produce mock observations only based on the fundamental physical laws given by the fitted cosmology. The goodness of fit of our model to the reality can thus be evaluated by comparing observations with their artificial counterparts. The result allows us to constrain the scales at which the physical laws yield a good understanding of reality. To build a bridge from ontology to epistemology, a collaboration to philosophers of science has been set up, to make implicit semantics explicit (Is dark matter a mere placeholder for missing mass?), elaborate on the metaphysical meaning of the constituents of our models (What is a particle in a cosmological simulation?) and sharply delimit the boundaries of our knowledge of the universe as bounded by observable evidence (How can we separate evidence-based properties of the universe from model-based estimates?).
Alternatively, we can interpret cosmology as an under-constrained optimisation problem. Fitting models then implies adding constraints until the problem is well-constrained. Instead, we can also reduce the amount of unknowns to those that can directly be determined by observables. The information that is gained in this way is the maximum information all model fits agree upon. It is also the maximum information that can be retrieved with the least amount of necessary assumptions in a given theoretical framework. The development of this approach is deeply rooted in mathematics, calculous, probability theory, morphometry and random geometric structures. Applying this approach to strong gravitational lensing being one common cosmological probe, we find local properties of the gravitational lens and, realising that lensing only probes correlated paths of a few lines of sight, we obtain the most general class of degeneracies inherent in the strong lensing theory.
Historical embedding
Dennis Sciama and his collaborators established this research direction in the second half of the last century. Since then, it has been further extended and applied to a multitude of observations. The increasing amount and quality of available data makes this approach an ideal framework to replace model assumptions by observational evidence. Rising tensions in our cosmological concordance model may thus be resolved.
