Supervisor: Sofie Marie Koksbang
Prerequisites: FT501 (Matematisk analyse). FY512 (Modellering af fysiske systemer). (Supervision can be in either English or Danish.)
Project type: The project is theoretical and will require both analytical and numerical work, with the major emphasis on whichever of these the student prefers. (The numerical work can be minimized to generating simple figures in e.g. matlab.)
Overall goal: Understand and explore the concept of cosmic backreaction.
Keywords: General relativity, Einstein's equations, cosmology
Project description:
According to the standard model of cosmology, about 70 % of the present-time content of the Universe consists of so-called "dark energy". Dark energy is introduced into the model mainly to induce a late time accelerated expansion of the Universe. The physical origin of dark energy is, however, completely unknown. One theory, the backreaction conjecture, posits that dark energy does not exist and that the apparent late-time accelerated expansion is an artifact due to the non-linearity of Einstein's equations: The non-linearity means that Einstein's equations give different results for the large-scale dynamics of the Universe depending on whether one plugs in average density fields etc. into Einstein's equations or instead plugs in the inhomogeneous density field (describing a universe with galaxy clusters, voids etc.) and averages afterwards (to get a set of equations describing the large-scale/smooth universe). The former is manifestly incorrect but it is what is done in standard cosmology. The latter is formally correct and gives extra terms sourcing the expansion of the Universe, including a term which can lead to accelerated expansion. A realistic quantification of cosmic backreaction of the real universe is still missing, but observations are hinting at a breakdown of standard cosmology. In the case of such an event, a cosmological model taking e.g. backreaction into account is a prime contender to take over as the standard model of cosmology.
The project will aim at describing and understanding the concept of cosmic backreaction. The project could for instance start with a derivation of the Buchert equations (analogous to the Friedmann equations) which govern the large-scale dynamics of an inhomogeneous universe, followed by an intuitive illustration of the backreaction effect using simple toy-models known as two-region models. If time remains, backreaction can afterwards be explored either numerically or analytically in different exact solutions to Einstein's equations.