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Higher order derivative gravitational theories in the metric and Palatini formalisms

Diekema, Jolien (2018) Higher order derivative gravitational theories in the metric and Palatini formalisms. Master's Thesis / Essay, Physics.

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Lovelock and galileon theories are known extensions of general relativity that have actions containing second order derivatives, but do not produce field equation with third or higher order derivatives. We show that the dimensional reduction of Lovelock results in a generalized covariant galileon theory. Then we explain the Palatini formalism, a way to consider gravity in non-Riemannian geometry. It is known general relativity can be obtained in both the metric and Palatini formalism. This gives us a motivation to study other higher order derivative theories in the Palatini formalism as well. The possibility of using dimensional reduction as a tool to learn more about the Palatini formalism is explored in this thesis but does not lead to interesting results. Then Palatini formalism is applied to the cubic covariant galileon. The field equation for the connection can be solved and is found to be the Weyl connection. Furthermore, we show that the physics change in the Palatini formalism and point out the importance of projective invariance and some kind of duality between torsion and non-metricity in the cubic covariant galileon framework.

Item Type: Thesis (Master's Thesis / Essay)
Supervisor name: Roest, D.
Degree programme: Physics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 05 Nov 2018
Last Modified: 06 Nov 2018 11:41

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