Dynamical systems in cosmology
| Thesis title in Czech: | Dynamické systémy v kosmologii |
|---|---|
| Thesis title in English: | Dynamical systems in cosmology |
| Key words: | dynamické systémy, kosmologie, temná hmota, temná energie |
| English key words: | dynamical systems, cosmology, dark matter, dark energy |
| Academic year of topic announcement: | 2017/2018 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Institute of Theoretical Physics (32-UTF) |
| Supervisor: | Giovanni Acquaviva, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 27.01.2017 |
| Date of assignment: | 27.01.2017 |
| Confirmed by Study dept. on: | 18.05.2018 |
| Date and time of defence: | 08.09.2020 09:00 |
| Date of electronic submission: | 29.07.2020 |
| Date of submission of printed version: | 29.07.2020 |
| Date of proceeded defence: | 08.09.2020 |
| Opponents: | Georgios Loukes Gerakopoulos, Dr. |
| Guidelines |
| - Review of existing literature
- study of recent cosmological models with dark matter and dark energy - development of new models of scalar field cosmology by choosing specific potentials - study of the properties of such models in the context of dynamical systems analysis |
| References |
| - A.A. Coley, Dynamical systems and cosmology. Vol. 291 (Springer Science & Business Media, 2013)
- J. Wainwright and G.F.R. Ellis., Dynamical systems in cosmology (Cambridge University Press, 2005) - E.J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15, 1753 (2006) - M. Goliath and G.F.R. Ellis, Homogeneous cosmologies with a cosmological constant, Phys. Rev. D 60, 023502 (1999) |
| Preliminary scope of work |
| Tématem práce je studium vlastností dynamických systémů v kontextu obecné teorie relativity se zvláštním důrazem na kosmologické aplikace. Převedením Einsteinových rovnic do tvaru autonomního dynamického systému je možné provést gobální analýzu celého prostoru řešení, včetně analýzy jejich stability v asymptotické limitě. Práce se zaměří na přehled známých modelů popsaných v existující literatuře a na popsání uvedené metody srozumitelným způsobem. Poté student rozšíří existující výsledky týkající se efektů temné hmoty a energie v prostoročasech s nízkým stupněm symetrie. |
| Preliminary scope of work in English |
| The scope of the thesis is to analyse the dynamical systems approach in the context of General Relativity, with particular emphasis on cosmological applications. By recasting Einstein's field equations in the form of an autonomous dynamical system it is possible to perform a global analysis of the whole space of solutions, including their stability in the asymptotic limits. The thesis will focus first of all on reviewing known models in order to provide a landscape of the existing literature and to present the method in a comprehensive way. Moreover, the work will possibily include original results regarding recent models describing the effects of dark matter and dark energy in low-symmetry spacetimes. |