Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.655920
Title: Constrained dynamics and higher derivative systems in modified gravity
Author: Chen, Tai-jun
ISNI:       0000 0004 5368 0505
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2015
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.655920  DOI: Not available
Keywords: Mathematics ; Physics ; General relativity ; Higher derivative theory ; Constrained dynamics
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