Research Projects
The group’s current projects turn broad questions about …
Dynamics of matter in the decelerated epoch
Project leader: David Fajman
Date: 01.04.2026 - 31.03.2030
In the early phases of cosmological evolution, the Universe expanded significantly more slowly than it does at present. The aim of this project is to understand how matter behaves during such a phase of slow expansion. This dynamics is particularly crucial for the emergence of structures in the present-day Universe. Specifically, we seek to determine the conditions under which matter homogenizes and when, by contrast, it condenses into structures. This is relevant for gaining an analytical understanding of the formation of cosmic structures such as galaxies and galaxy clusters, and for elucidating the mechanisms by which this process occurs. The starting point of our investigation is a recently discovered critical phenomenon in fluids that, depending on the expansion rate of the Universe, either homogenize or form shocks and thus structures. Using a hybrid approach that combines rigorous mathematical analysis with high-precision numerical simulations, we will investigate these phenomena under general conditions, with the goal of understanding the consequences of these effects for realistic cosmological scenarios. This hybrid methodology particularly reveals nonlinear effects that remain hidden to purely linear methods and provides a comprehensive picture of the actual behavior of matter. In particular, we will examine the conditions under which generic fluids in slowly expanding phases homogenize or form shocks. To this end, we will consider equations of state that have not previously been studied in the context of this phase transition between stability and instability, such as polytropic fluids, in order to understand how material properties influence the transition. In addition, we will analyze the influence of spacetime curvature on stability and shock formation in fluids, as this is especially relevant in the relativistic regime for applications in cosmology. Moreover, we will consider fluids with additional interactions, especially gravity and electromagnetism. From a heuristic perspective, gravity favors shock formation, while electric repulsion counteracts it. Because the fluid model breaks down at shocks, we will also consider the Vlasov model, in which the matter itself is collisionless. This model is used to describe matter on large scales, such as in galaxies or galaxy clusters. We will compare the dynamics of Vlasov matter with those of fluids to better understand how interactions within the fluid affect structure formation. Our goal is an integrated picture of matter dynamics that shows when matter in a slowly expanding Universe remains homogeneous and when it forms structures. This will fundamentally contribute to developing a comprehensive, definitive understanding of early structure formation in the cosmos.
Funded by: FWF
"Dynamics of matter in the decelerated epoch" @FWF
Matter dominated cosmology
Project leader: David Fajman
Date: 01.01.2025 - 31.12.2029
Cosmology investigates questions about the origin, the evolution and the future development of the universe. Several scientific disciplines of physics contribute to these investigations. Restricting oneself to those aspects of cosmology that are purely governed by gravitation, then Einsteins equations are, according to current understanding, the system that describes the behaviour of the universe accurately. They provide the opportunity to consider models of the universe mathematically rigorous including those types of matter models that behave realistically in the case of low particle densities. Among those types of systems the Einstein-Vlasov system is the one that is mathematically best understood. It is this system we investigate rigorously in this research program. It is the aim of the discipline of Mathematical Cosmology to make rigorous statements about the structure of solutions of Einstein-matter systems by studying the Einstein equations using modern mathematical methods and to understand possible scenarios for the cosmological evolution. Particularly relevant are stability results of certain spacetimes, which confirm that those models may describe the generic behaviour of spacetime. In the envisioned research project we focus on one particular aspect of this general program, which we motivate in the following. Fundamental results in the area of Mathematical Cosmology concern exclusively those models of spacetime, whose long-time behaviour is similar to those of the pure vacuum equations. Consequently, in those models, matter has no fundamental influence on the geometry of spacetime on large scales. However, there exist certain solutions of Einsteins equations coupled to realistic matter models, whose long-time behaviour is determined by the matter. We call those solutions matter dominated. For the Einstein-Vlasov system there are two classes of such matter dominated models, the Einstein- deSitter solution and the Rendall class. Both solutions described expanding universes. It is the aim of the research program to investigate the asymptotic behaviour near those models. We study those system by different methods starting with numerical simulations in a symmetry reduced setting. Starting from those results we apply a series of analytical methods to establish the numerical findings rigorously. We will then use the numerical infrastructure to simulate those systems for more general classes of initial data and to obtain information on their long-time behaviour. Those investigations concern the case of large data, i.e. highly inhomogeneous perturbations of spacetime. This regime of Einsteins equations is also almost completely non-understood from an analytical point of view. Finally, we will study singularity formation of this systems, which is relevant for big-bang formation in those models, where we include extensions of our system to include electromagnetism and collisions of particles.
Funded by: FWF
"Matter dominated cosmology" @FWF
Lensing of electromagnetic and gravitational waves
Project leader: Marius Adrian Oancea
Date: 01.11.2025 - 31.10.2029
This project explores how light and gravitational waves travel through the universe, in particular when their paths are distorted by the gravitational field of massive cosmic objects such as black holes or galaxies. An effect known as gravitational lensing can magnify, shift, or even duplicate the images of distant sources. This offers astronomers powerful tools to observe faraway objects and to study how gravity operates in extreme conditions. While gravitational lensing is a well-established phenomenon, most models assume that the sources and lenses do not move and that waves behave like simple rays of light. This project challenges those assumptions by investigating what happens when we account for motion, wave effects, and the strong gravitational fields found near black holes. One aim is to understand how the apparent position and color (redshift) of a distant light source changes over time due to lensing by moving objects. These small shifts, normally too subtle to be detected, may become greatly amplified when a source lies near a caustica region where the lensing effect is particularly strong. By modeling these effects and estimating their size under realistic conditions, this project will assess whether future observations could use them to detect sideways motion in faraway cosmic sources. This could offer a new way to measure the movement of distant galaxies or quasars, deepening our understanding of the structure and evolution of the universe. At the same time, the project investigates how gravitational wavesripples in spacetime created by violent cosmic eventsare affected by strong gravitational lensing. In particular, we focus on systems where two black holes merge while orbiting a much larger black hole. These so-called hierarchical systems create complex wave signals that are bent and modified as they pass near the massive object. By simulating how these waves are distorted, the project aims to predict how such signals would look like to gravitational wave detectors on Earth. This may help astronomers recognize such systems in real data and learn more about the environments in which black holes grow and merge. To fully capture the behavior of waves in such extreme settings, the project will also develop a new mathematical approach that goes beyond traditional ray-based models. Inspired by techniques from quantum physics, this approach uses a tool called the Wigner function to describe how waves evolve when interference and diffraction become importantparticularly near caustics, where previous models break down. Applying this framework to curved spacetime will make it possible to study wave effects that were previously out of reach and may lead to more accurate predictions in a wide range of astrophysical situations. Together, these efforts aim to expand the tools available to modern astrophysics, offering a more complete picture of how light and gravity interact across vast cosmic distances and under extreme physical conditions.
Funded by: FWF
“Lensing of electromagnetic and gravitational waves” @FWF
Frequency and polarization-dependent lensing of gravitational waves from hierarchical triple black hole systems
General Relativistic Accelerated Motion
Project leader: Hamed Barzegar
Date: 01.09.2024 - 31.08.2027
Since Newton discovered his laws of motion and gravitation, the understanding of motion, especially acceleration and deceleration, has become crucial. He and his followers extended these ideas to non-inertial frames. A significant advancement was the investigation of motion in Einstein`s Special Relativity, particularly accelerated motions over very short time intervals. A common example is an object moving with constant acceleration. However, to fully grasp dynamics, we need Einstein`s General Relativity (GR), which includes the effects of gravity and how masses curve space. There has been little research so far on accelerated motion in the curved spacetime of GR in general. This project aims to develop a new framework to understand this by examining different spacetime geometries to study motions of matter not aligned with the flow of spacetime. It aims to establish a connection between the Newtonian gravitation and GR to explain specific gravitational effects. Initially, a comprehensive analytical framework for such "tilted" spacetimes will be developed, before specific cases like those considered in `warp-drive` spacetimes are explored in depth. Current studies often neglect the significance of tilted and accelerated motion in these spacetimes, leading to unrealistic models. The goal is to devise a method to address these issues and answer open questions. The project will also investigate cosmological problems such as the flow of large galaxy groups and discrepancies in measurements of the Universe`s expansion rate. The developed models should be flexible enough to capture both large-scale and local cosmic structures, unlike existing models that often focus on a single scale only. Some of these models may also be relevant to theories involving faster-than-light travel. Various ideas will be explored, including a theory that extends Newtonian gravitation to include effects predicted uniquely by GR, such as gravitoelectromagnetism. Motion in cosmological models is often associated with a dipole, thus exact solutions of GR that include a dipole structure like the Szekeres class will be examined. The Lyon team has developed tools for detailed modeling of large- scale structures in both Newtonian and Einsteinian cosmology, which will aid in understanding patterns in the Universe detected by ongoing and forthcoming observational programs of supernovae and highly redshifted galaxies. This project lies at the intersection of various research fields and benefits from combined knowledge in these areas.
Funded by: FWF
“General Relativistic Accelerated Motion” @FWF
A Lagrangian description of a T-Warp proposed by H. Barzegar and T. Buchert
Scattering near cosmological spacetimes
Project leader: Liam Dylan Urban
Date: 17.08.2026 - 16.08.2029
Erwin Schroedinger program
Funded by: FWF
“Scattering near cosmological spacetimes” @FWF
Cosmological Fluid Models Beyond the Critical Regime
Project leader: Maximilian Ofner
Date: 01.05.2026 - 30.04.2029
Erwin Schroedinger program
Funded by: FWF
“Cosmological Fluid Models Beyond the Critical Regime” @FWF