Cosmological dynamics of exponential gravity

Master Thesis


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University of Cape Town

The objective of this thesis is to explore several hotly debated current issues in modern cosmology, with a focus on f(R) gravity. In chapter 1 we present a review of modern theoretical cosmology. We begin by introducing some fundamental cosmological concepts, followed by a discussion of the field equations of general relativity, which underlie both the behavior of global cosmological models and the isolated gravitating systems such as stars, black holes and galaxies. In particular we focus on the solutions for the Friedmann-Robertson-Walker Universe. Next we present a detailed discussion of the dark matter problem. Astrophysical observations indicate that the two components account for 25% of the total mass/energy of the observable Universe. We then present the big bang model, which represents the current standard model for the origin and the evolution of the Universe. In our discussion we introduce the inflationary scenario in some detail; specifically we present an example of quadratic inflation to demonstrate how this scenario provides a solution to some of the problems with the standard model. Next we discussed the dark energy model, which as been introduced to address the late-time acceleration problem. We then present the quintessence model, which as been proposed to address the coincidence and the magnitude problems. We conclude this chapter by a detailed discussion of the higher order theories of gravity with a particular we focus on f(R)-gravity, which is based on the idea of introducing corrections to the Einstein-Hilbert action that are negligible in the early Universe and only become effective at late times when the Ricci curvature R decreases. In our discussion we indicate how these corrections can be interpreted as an effective fluid of purely geometrical origin; we also discuss the phase space and stability of deSitter space in f(R) gravity.

Includes abstract.

Includes bibliographical references (p. 69-73).