World Models

Cosmology Gravity is the only interaction relevant on cosmological scales. Gravity is best described by the General Theory of Relativity (GR). Physical world models must thus be constructed from GR. This is greatly simplified by two symmetry assumptions:
  • The Universe is isotropic around us, i.e. we observe the same mean properties of the Universe in all directions.
  • There are no preferred observers in the Universe. Accordingly, the Universe is isotropic around each point (otherwise we would be preferred), and thus it is also homogeneous.
Such highly symmetric solutions to Einstein's field equations were first constructed by Alexander Friedmann. Because of homogeneity and isotropy, they can only depend on time. They describe the temporal change of the so-called scale factor, which quantifies by how much space is expanding or shrinking.

These Friedmann models are unstable and thus expand or contract. In order to enable static world models, Einstein introduced the cosmological constant before Hubble discovered that the Universe is actually expanding.


The Friedmann models are characterised by several parameters. Among them are the total matter density, the radiation density, the cosmological constant and the present-day relative expansion rate of the Universe, termed Hubble constant. The behaviour of the Friedmann models depends sensitively on these parameters. Their measurement is one of the central goals of cosmology.

The Microwave Background

CMB The Universe was much smaller in the past than today, and thus much hotter. It contained photons which initially scattered off the charged particles in the cosmic plasma. When the Universe had cooled to 3,000 degrees Kelvin, atoms formed and the photons could propagate almost freely. They lost energy due to the expansion of the Universe, cooled accordingly to almost 3 degrees Kelvin until the present, but surround us in form of a cosmic microwave background (CMB).

WMAP Present-day structures in the Universe were already seeded when the CMB was set free. Tiny structures were thus imprinted onto the CMB temperature. Cosmological parameters can be precisely measured from the statistical properties of these fluctuations. Currently, the American WMAP satellite (right-hand image) is observing the microwave sky. First results (top-left image) show that the Universe is spatially flat, originated 14 billion years ago and consists to one third of dark matter. The rest is contributed by the cosmological constant or some other form of dark energy.

Cosmic Consistency

Evolution The results are supported by a multitude of other cosmological experiments: Supernovae of type Ia support the dominating role of the cosmological constant, gravitational lenses confirm the amount of dark matter, galaxy clusters would have developed much later only, the way how the galaxy distribution is structured hints at the same low matter density, and so on. For the first time in the history of physical cosmology, there exists a precisely determined standard model.

Open Questions

The Big Bang model is thus impressively confirmed, but only at the expense of big, unsolved questions. The most important of those are:

What is dark matter made of? It is highly probable that it is composed of weakly interacting elementary particles. Those cannot be the neutrinos, however, because structures smaller than galaxy clusters could hardly have formed. By far the most successful model is that of Cold Dark Matter (CDM).

What is the physical meaning of the cosmological constant? What is the dark energy? The universe expands in an accelerated way, which is enabled by the cosmological constant in the context of the Friedmann models. One possible reason are appropriately self-interacting scalar fields (quintessence, dark energy).

Structures How did structures form in the Universe? We understand how the diversity of structures could grow in the Universe, but not where they came from. The model of cosmological inflation explains the origin of cosmic structures from quantum fluctuations in the very early Universe. The right-hand image shows a numerical simulation of structure growth in dark matter.

Why is the CMB so highly isotropic? The CMB was formed approximately 400,000 years after the Big Bang. Up until then, such regions could not be in causal contact which were separated by more than 400,000 light years. Nonetheless, the CMB temperature is almost the same across the whole sky. How was that possible? Cosmological inflation offers an answer to that question, too.

How do structures of completely different scales develop? How did the first stars, galaxies, black holes, galaxy clusters and so on form in a Universe dominated by dark matter and dark energy? How does the little light that we see allow drawing conclusions on dark matter and dark energy?

Verantwortlich: Matthias Bartelmann