Browsing by Author "Tema, Seturumane"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Open Access
    A Lagrangian formulation of a theory of a scalar field superfluid dark matter
    (2022) Tema, Seturumane; Larena, Julien; Osano, Bob
    In this thesis we discuss the dynamics of the relativistic Lagrangian of the theory of dark matter superfluidity. The second and third chapters of the thesis are a review. In the fourth chapter we show that a complex scalar field whose dynamics are dictated by such a Lagrangian, models dust in the background universe on cosmological scale. Prior to our calculations, the theory was shown to model dust on cosmological scale and a superfluid on galactic scale in the non-relativistic case [1]. This project, extends the non-relativistic theory, to include the relativistic background. We continued, using the relativistic Lagrangian, to investigate how perturbations of such a theory grow in a perturbed universe, and found that the density contrast (of the theory) is constant when the complex scalar field is not coupled to baryons in the weak-field limit.
  • No Thumbnail Available
    Item
    Open Access
    A study of the cosmological singularity from modified gravity
    (University of Cape Town, 2026) Tema, Seturumane; Haque, Shajid; Das, Saurya
    This thesis investigates the resolution of the Big Bang singularity within classical extensions of General Relativity (GR). In GR, the singularity cannot be avoided without violating classical energy conditions; spacetime curvature becomes unbounded in the early Universe, and geodesics terminate in finite affine parameter, preventing a complete classical description of cosmic evolution. Two main strategies have been proposed to address this problem: replacing GR with a theory valid at high curvatures, or invoking quantum gravity, where non-classical effects dominate the earliest moments of cosmic evolution. We pursue the former, focusing on higher-curvature modifications of GR, particularly f(R) gravity, and on scalar–tensor extensions such as Brans–Dicke theory, which is dynamically related to f(R). Our analysis proceeds along two complementary approaches. First, by applying the time-like and null Raychaudhuri equations in a Friedmann–Lemaître–Robertson–Walker (FLRW) background, we show that power-law scale factor solutions, a(t) ∼ tα, in Brans–Dicke theory and f(R) gravity naturally lead to defocusing of geodesics in both the ekpyrotic regime (α < 1/3) and the accelerating regime (α > 1). This demonstrates that singularity formation can be avoided by considering the evolution of a congruence of geodesics without violating standard energy conditions. Second, using a compact, model-independent dynamical systems formulation of f(R) gravity, we show that non-singular bouncing solutions arise generically in these same regimes. In both dust and radiation-dominated universes, phase-space trajectories cross the bounce surface smoothly, confirming that the Universe can transition from contraction to expansion without encountering geodesic incompleteness. The agreement between the Raychaudhuri analysis and the dynamical systems framework highlights the robustness of singularity resolution within extended gravity theories. The central result of this thesis is that higher-curvature modifications, specifically f(R) gravity and its scalar–tensor counterpart, permit consistent power-law bouncing cosmologies that evade the classical Big Bang singularity while respecting energy conditions.