Extended theories of gravity: the early universe and stellar interiors

Campbell, Mariam

Extended theories of gravity: the early universe and stellar interiors

Thesis / Dissertation

2026

Publisher

University of Cape Town

Department

Department of Mathematics and Applied Mathematics

Faculty

Faculty of Science

Abstract

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.

Keywords

mathematics

Reference:

Collections

PhD / Doctoral

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