Extended theories of gravity: the early universe and stellar interiors

dc.contributor.advisorDunsby, Peter Klaus
dc.contributor.authorCampbell, Mariam
dc.date.accessioned2026-06-17T09:15:46Z
dc.date.available2026-06-17T09:15:46Z
dc.date.issued2026
dc.date.updated2026-06-17T09:13:03Z
dc.description.abstractThis thesis explores two central themes within extended theories of general relativity: the cosmological dynamics of the early universe and the formulation of mathematical frameworks for modeling relativistic stars, with the overarching aim of testing and constraining model parameters in modified gravity. In the cosmological context, a perturbative analysis of scalar-tensor theories demonstrates that a stable bi-scalar tensor model can yield a cosmic bounce preceding natural inflation. A detailed dynamical systems study of a Dirac–Born–Infeld (DBI) field further shows that initial conditions favorable to a bounce become increasingly likely as the system approaches the ultrarelativistic limit. A key result, derived for the first time in a spatially closed Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime, reveals that the introduction of a negative cosmological constant does not lead to cyclic behavior in the DBI framework, implying that additional exotic degrees of freedom may be necessary to achieve cyclicity. In the study of relativistic stars, this thesis presents two new exact, physically viable solutions to the Tolman–Oppenheimer–Volkoff (TOV) equations within extended gravity models. For theories with a quadratic correction to the Einstein–Hilbert action, the solutions describe (1) a quasi-isotropic stellar configuration with a shell and double-layer structure resembling a dipole distribution, and (2) a configuration characterized by a quartic correction to the Newtonian potential and a smooth boundary matching. These results highlight the effectiveness of analytical methods in capturing the astrophysical behavior of compact objects in modified gravity. Moreover, the structural and compositional differences identified in these stellar models, relative to standard general relativity (GR), suggest potentially observable signatures that could be probed by future astrophysical observations.
dc.identifier.apacitationCampbell, M. (2026). <i>Extended theories of gravity: the early universe and stellar interiors</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/43324en_ZA
dc.identifier.chicagocitationCampbell, Mariam. <i>"Extended theories of gravity: the early universe and stellar interiors."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2026. http://hdl.handle.net/11427/43324en_ZA
dc.identifier.citationCampbell, M. 2026. Extended theories of gravity: the early universe and stellar interiors. . University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/43324en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Campbell, Mariam AB - This thesis explores two central themes within extended theories of general relativity: the cosmological dynamics of the early universe and the formulation of mathematical frameworks for modeling relativistic stars, with the overarching aim of testing and constraining model parameters in modified gravity. In the cosmological context, a perturbative analysis of scalar-tensor theories demonstrates that a stable bi-scalar tensor model can yield a cosmic bounce preceding natural inflation. A detailed dynamical systems study of a Dirac–Born–Infeld (DBI) field further shows that initial conditions favorable to a bounce become increasingly likely as the system approaches the ultrarelativistic limit. A key result, derived for the first time in a spatially closed Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime, reveals that the introduction of a negative cosmological constant does not lead to cyclic behavior in the DBI framework, implying that additional exotic degrees of freedom may be necessary to achieve cyclicity. In the study of relativistic stars, this thesis presents two new exact, physically viable solutions to the Tolman–Oppenheimer–Volkoff (TOV) equations within extended gravity models. For theories with a quadratic correction to the Einstein–Hilbert action, the solutions describe (1) a quasi-isotropic stellar configuration with a shell and double-layer structure resembling a dipole distribution, and (2) a configuration characterized by a quartic correction to the Newtonian potential and a smooth boundary matching. These results highlight the effectiveness of analytical methods in capturing the astrophysical behavior of compact objects in modified gravity. Moreover, the structural and compositional differences identified in these stellar models, relative to standard general relativity (GR), suggest potentially observable signatures that could be probed by future astrophysical observations. DA - 2026 DB - OpenUCT DP - University of Cape Town KW - mathematics LK - https://open.uct.ac.za PB - University of Cape Town PY - 2026 T1 - Extended theories of gravity: the early universe and stellar interiors TI - Extended theories of gravity: the early universe and stellar interiors UR - http://hdl.handle.net/11427/43324 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/43324
dc.identifier.vancouvercitationCampbell M. Extended theories of gravity: the early universe and stellar interiors. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2026 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/43324en_ZA
dc.language.isoen
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.publisher.institutionUniversity of Cape Town
dc.subjectmathematics
dc.titleExtended theories of gravity: the early universe and stellar interiors
dc.typeThesis / Dissertation
dc.type.qualificationlevelDoctoral
dc.type.qualificationlevelPhD
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