Reacting to Stage IV data: A unified and scalable framework for cosmic shear and galaxy cluster statistics in Horndeski gravity

• Applicant: Matteo Cataneo, Ph.D.
• Subject Area: Astrophysics and Astronomy
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 573007574

Understanding the origin of the observed late-time cosmic acceleration remains one of the central open questions in cosmology. In the standard cosmological model (ΛCDM), this accelerated expansion is attributed to the cosmological constant (Λ)—a simple term in Einstein’s field equations consistent with the symmetries of General Relativity. However, arguments grounded in quantum field theory render this explanation theoretically unsatisfying. Horndeski gravity, a broad class of scalar-tensor theories, is an appealing alternative in which a dynamical scalar field drives the acceleration while potentially avoiding the fine-tuning problems associated with Λ. This field can also mediate a fifth force, altering both the growth of cosmic structures and the propagation of light. These effects leave characteristic signatures on the formation, evolution, and appearance of structure in the Universe, offering a promising avenue to test departures from the standard model. The next generation of sky surveys, led by the European Euclid mission and the Vera C. Rubin Observatory, will map the positions and shapes of billions of galaxies with unprecedented precision and detect hundreds of thousands of galaxy clusters. Cosmic shear—the coherent distortion of galaxy shapes by large-scale structure through weak gravitational lensing—and the abundance, spatial distribution, and internal profiles of galaxy clusters are all highly sensitive to departures from standard gravity. For general Horndeski models, however, accurate predictions on the scales most relevant to these observations—where the signal-to-noise ratio is highest—are still lacking. Current approaches either rely on computationally expensive simulations for a limited set of models or restrict the analysis to large, linear scales, thereby limiting the constraining power of the data. To fill this gap, the proposed project will advance the Reaction Framework—a method that strategically combines first-principles and semi-analytical modelling with machine learning to predict the impact of physics beyond ΛCDM on small, non-linear scales. Since structure formation at these scales is also shaped by non-gravitational processes, the project will incorporate the effects of baryonic physics—such as AGN feedback and star formation—into the Reaction Framework, including potential couplings with Horndeski gravity. Modelling these effects within a unified framework will enable consistent theoretical predictions across all observables and help mitigate leading sources of systematic uncertainty in cosmic shear and cluster analyses. Finally, to capture information beyond what is accessible to two-point statistics, the project will deliver theory-based predictions for the one-point probability distribution of the weak lensing convergence field in Horndeski gravity. Together, these developments will enable more powerful and robust tests of gravity using data from the next generation of cosmological surveys.

• DFG Programme: Research Grants