The last three decades have witnessed the transformation of physical cosmology to a quantitative scientific discipline with the development of a standard model of the Universe's dynamics and geometry on large scales and a theory of cosmic structure and structure formation, both based on general relativity as a theory of gravity. This model asserts that cosmic structures have been seeded by inflation in the early universe and that structure formation proceeds by gravitational collapse of seed structures while the Universe expands in a homogeneous and isotropic way.
While this standard model is presently viable and in agreement with current observations, there are many unclear questions, one important among them concerns the properties of gravity on Gpc-scales, where general relativity predicts gravity to becomes repulsive and to accelerate the expansion of the Universe. This has been experimentally shown by observing distant supernovae which are systematically dimmer than expected in a non-accelerating Universe. The origin of acceleration is attributed to a cosmological constant, which appears naturally in general relativity and whose effects appear on large, cosmological distances by changing the distance-redshift relation of supernovae and by affecting structure growth.
Whether the cosmological constant or an alternative mechanism is responsible for the Universe's accelerated expansion is a subject of current research: The most basic extensions to the standard model construct dark energy as scenarios that allow time evolution. Couplings between dark matter and energy, or with neutrinos are proposed to overcome 'coincidences' that lack explanations within the standard model. Another avenue are modifications of general relativity on large scales: Additional nonlinear terms in the gravitational interaction may weaken gravity on large scales and make accelerated expansion possible while on small scales or in regions of large densities general relativity is recovered by screening mechanisms.
The properties of cosmic structures are to a large degree determined by those of dark matter while on small scales below 1 Mpc the influence of baryons becomes important, and eventually dominant. The dark matter distribution of gravitationally bound cosmic structures is routinely recovered in numerical simulations, but from a fundamental point of view, it is still unclear why the structures have this shape and why they are stable. While these problems are unsolved even for the most basic dark matter models with standard Newtonian gravity, they remain even less clear if there are couplings between dark matter, baryonic matter and dark energy, or for modifications of the gravitational law.
Common to these ideas is the search for new fundamental gravitational phenomena as the investigation of the properties of gravity on the relevant scales has only become possible in the last decades through observations of supernovae of type Ia, large-scale galaxy surveys and the cosmic microwave background. These three particular probes have focused on the geometry of the Universe and have provided information about the initial conditions of structure formation. But apart from geometrical probes it is attractive to investigate properties of gravity by its influence on the formation of cosmic structures. These observations would use the weak gravitational lensing effect by the large-scale distribution of matter and observations of baryon acoustic oscillations in the galaxy distribution, which are two of the primary tasks of future large-scale surveys like the European Euclid-satellite mission, the ongoing Dark Energy Survey and the planned Large Synoptic Sky Telescope. Advances in observational techniques will enable detailed investigations of the internal dynamics of bound structures and will potentially uncover the relation between their properties and the properties of dark matter particles, possible coupling to dark energy, or changes in the effective gravitational law which they may be subjected to.
It is clear that future investigations of gravity on large scales will not be limited by statistics as Euclid will essentially observe the Hubble volume. Instead, all observations will be limited by systematics, i.e. by incompletely understood properties of the observed objects. But in order to make use of structure formation as a probe of gravity it is vitally important to understand the astrophysics of cosmic structure formation, otherwise the potentially exquisite sensitivity on properties of gravity can not be unlocked. Our proposal is specifically targeted at this issue. We have identified a number of problems in which an incomplete understanding of astrophysics stands in the way of performing cosmological observations and of understanding the properties of gravity on large scales, and where the astrophysical problem itself it a rich and rewarding topic.