## Constrained dynamics and higher derivative systems in modified gravity

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##### Authors

Chen, Tai-jun

##### Advisors

Lim, Eugene

##### Date

2015-06-09##### Awarding Institution

University of Cambridge

##### Author Affiliation

Department of Applied Mathematics and Theoretical Physics

##### Qualification

PhD

##### Language

English

##### Type

Thesis

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Show full item record##### Citation

Chen, T. (2015). Constrained dynamics and higher derivative systems in modified gravity (doctoral thesis).

##### Abstract

In this thesis, higher derivative theories and constrained dynamics are investigated in detail. In the first part of the thesis, we discuss how the Ostrogradski instability emerges in non-degenerate higher derivative theories in the context of a one-dimensional point particle where the position of the particle is a function only dependent on time. We show that the instabilities can only be removed by the addition of constraints if the original theory’s phase space is reduced. We then generalize this formalism to the most general higher derivative gravity theory where the action is not only linearly dependent on the Ricci scalar but also the quadratic curvature invariants in four-dimensional spacetime. We find that the instabilities can be removed by the judicious addition of constraints at the quadratic level of metric fluctuations around Minkowski and de Sitter backgrounds while the dimensionality of the original phase space is reduced. The constrained higher derivative gravity theory is ghost free as well as preserves the renormalization properties of higher derivative gravity, at the price of giving up the Lorentz invariance. In the second part of the thesis, we study the spherically symmetric static solution of a class of two scalar-field theory, where one of them is a Lagrange multiplier enforcing a constraint relating the value of the other scalar field to the norm of its derivative. We find the spherically symmetric static solution of the theory with an exponential potential. However, when we investigate the stability issue of the solution, the perturbation with the odd type symmetry is stable, while the even modes always contain one ghostlike degree of freedom.

##### Keywords

Mathematics, Physics, General relativity, Higher derivative theory, Constrained dynamics

##### Identifiers

This record's URL: http://www.repository.cam.ac.uk/handle/1810/248757