all projects

sampling methods and physics of MCMC


Monte-Carlo Markov-chain methods are widely (and wildly) used in cosmological inference and can always be mapped back onto a canonical, statistical physics system. Interesting questions we pursue concern canonical parition functions reflecting cosmological, non-Gaussian likelihoods and analytical methods for inference for these cases.

lecture notes


Since 2022 I am writing up my lecture notes, and hope that there will be a full series on theoretical physics in the future, with a consistent notation, published under a creative common license, and distributed free of charge through Heidelberg University Publishing.

information theory and inference


Information entropies (like Kullback-Leibler or Rényi entropies) are measures of statistical randomness of distributions, if applied to the posterior of a distribution they serve as a quantification of remaining statistical uncertainty, i.e. how well measurements have been able to improve the knowledge on a given physical model. We work on the connection between more conventional tools in statistics and inference such as likelihoods and statistical tests, with novel concepts like information entropies, with an application to cosmological data sets.

machine learning in cosmology and beyond


Machine learning methods can help infering fundamental laws of Nature from complex data or to design inference processes that are otherwise difficult to manage. We are trying to apply inference on inflationary potentials with machine learning methods and hopefully establish links to information geometry.

gravity on large scales


We work on the design of tests of specific, non-standard tests of gravity on galactic scales like screening-mechanisms. Furthermore, we investigate possible signatures of post-Newtonian gravity in cosmological surveys, and how general relativistic effects can be observed in cosmology.

axion dark matter


Axions and axion-like particles are an interesting alternative to dark matter on the TeV-scale and should show new phenomena on small scales. Their very light masses cause their wave function to have de Broglie-wavelengths comparable to the size of cosmological objects such as dwarf galaxies, with less substructure on small scales and a density core as a natural consequence. With T. Schwetz-Mangold (KIT) and J. Jaeckel (Heidelberg) we are investigating signatures of axion dark matter. This requires to do quantum mechanics in gravitational fields and find analogues to classical concepts like gravitational collapse or virialisation for quantum mechanical, self-gravitating systems.

3D reconstructions


The phase-space of the cosmic large-scale structure is only partially accessible to observations. The resolution of structures along the line of sight is particularly difficult in weak lensing observations, but also in galaxy surveys one deals with rather large radial uncertainties. For that purpose, we employ 3d-decompositions and investigate the observability of 3d-Fourier modes, in weak lensing and in cross-correlation with other tracers, and compute effects that are sensitive to large-scale velocity fields.

constructive cosmology


Constructive gravity asserts that there is a clear path of constructing a gravitational interaction for particles that is determined completely by their non-gravitational interactions. Our group works in cooperation with F.P. Schuller (Erlangen) and M.C. Werner (Kyoto) on cosmological tests of constructive gravity, and we work on astrophysical and cosmological applications of area-metric gravity, as well as on its conceptual construction.

cosmic inflation


Cosmic inflation is an early phase of accelerated expansion that solves the flatness-problem in FLRW-cosmologies and is a mechanism for introducing fluctuations in the distribution of matter. Of particular interest to us are inflationary non-Gaussianities and their measurement in future large-scale structure surveys. The best way of measuring higher-order non-Gaussianities is still unclear; while there is a clear way of computing polyspectra from covariant perturbation theory, their estimation from data quickly becomes a combinatorial problem, for which we use advanced sampling methods.



The European Euclid mission is a space-based large-scale structure survey, where we are involved in the weak lensing programme, where we construct and test models of intrinsic alignments of galaxies, which result due to tidal interaction with the large-scale structure or by correlations in the initial conditions of structure formation. In addition, our group was active in computing second order effects in gravitational lensing, parameter estimation biases and the information content of Gaussian and non-Gaussian weak lensing maps.



The fluctuation pattern of the temperature and polarisation of the cosmic microwave background gets distorted by weak lensing deflection and changes therefore its correlation properties. Our group is interested in higher-order effects in lensing and cross-correlations between the lensing effect and other probes of the cosmic large-scale structure. From a methodical point of view closely related is the question of lensing of the 21cm background, which however involves more aspects of non-Gaussianity and reionisation history, including its non-uniformity.

statistical inference and information geometry


Modern cosmology is a statistical science and we are interested in questions related to the information content of large-scale structure surveys, in particular in the nonlinear regime, selection of models and the effect of systematical errors on the parameter estimation and model selection process. In particular, we investigate what properties about gravity are in principle knowable from cosmological surveys, how non-Gaussian structures can be described in an efficient way and how information about fundamental physics can be extracted from non-Gaussian structures.

weak gravitational lensing


Weak lensing refers to the weak distortion of the light bundles reaching us from distant galaxies caused by tidal gravitational fields in the cosmic large-scale structure. Weak lensing is an excellent tool for investigating gravity on large scales, and we have worked on tomographic methods, cross-correlations and higher-order statistics of the weak lensing signal, as well as effects gravitational light deflection at second order. We would like to understand how one can reach a precision prediction of the weak lensing signal, how one can use the lensing signal as a cosmoogical probe, and what statistical properties the lensing signal has.

intrinsic alignments


Weak lensing operates under the assumption of intrinsically uncorrelated galaxy shapes, which might not be true because galaxies experience correlated tidal gravitational fields and share a similar angular momentum generation. We have worked on tidal interaction models for galaxies to derive ellipticity correlations for investigating their contaminating effect in weak lensing parameter inference. Starting from models of tidal shearing and tidal torquing for the orientation of elliptical and spiral galaxies, we are constructing more elaborate models for predicting and investigating intrinsic alignments, and hope to apply them to Euclid data.

spherical collapse


Spherical collapse of a halo is one of the few instances where the fully nonlinear, relativistic equations of motion can be solved. In particular, our group has worked on collapse in non-standard gravitational models and computed the influence of tidal shear fields, split up into shear and vorticity, on the collapse dynamics. The overdensity needed for spherical collapse allows the prediction of number densities of expected haloes in a cosmic volume, and constraints on cosmological parameters as well as on the gravitational interaction from that quantity.

integrated Sachs-Wolfe effect


The iSW-effect is a secondary CMB-anisotropy and can be used to measure the equation of state of dark energy. Our results on the iSW-effect include the extension to nonlinearly evolving structures (Rees-Sciama-effect), the interpretation of the iSW-effect as a higher-order lensing phenomenon and cross-correlations with the weak lensing field. Using data from the European Planck-satellite, we have obtained independent measurements on the existence and properties of dark energy.



The Planck-surveyor satellite was a European CMB-mission that mapped out the temperature and polarisation fluctuations to angular scales of a few arcminutes. We added Sunyaev-Zel’dovich simulations to the Planck-sky model, as well as adopting maps of the vibrational transitions of carbon monoxide and of the free-free-emission due to direct interaction between electrons. In analysing the data, we obtained independent information on dark energy from the measurement of the integrated Sachs-Wolfe effect (together with P. Vielva and C. Hernandez-Monteagudo).



The Sunyaev-Zel’dovich effect describes a tiny transfer of thermal or kinetic energy from the hot intra-cluster medium of a galaxy cluster to the cold cosmic microwave background. It is a tool for detecting clusters of galaxies out to very high redshift, and provides a diagnostic of the relationship between temperature and mass of clusters. In addition, the kinetic Sunyaev-Zel’dovich effect arises due to a minuscule transfer of kinetic energy from the galaxy cluster’s electrons to the CMB photons, if the cluster is not at rest in a frame in which the CMB appears isotropic.