Scalar Fields and Alternatives in Cosmology and Black Holes

Extensions to general relativity are often considered as possibilities in the quest for a quantum theory of gravity on one hand, or to resolve anomalies within cosmology on the other. Scalar fields, found in many areas of physics, are frequently studied in this context. This is partly due to their manifestation in the effective four dimensional theory of a number of underlying fundamental theories, most notably string theory. This thesis is concerned with the effects of scalar fields on cosmological and black hole solutions. By comparison, an analysis of an inhomogeneous cosmological model which requires no extensions to general relativity is also undertaken. In chapter three, examples of numerical solutions to black hole solutions, which have previously been shown to be linearly stable, are found. The model includes at least two scalar fields, non-minimally coupled to electromagnetism and hence possesses non-trivial contingent primary hair. We show that the extremal solutions have finite temperature for an arbitrary coupling constant. Chapter four investigates the effects of higher order curvature corrections and scalar fields on the late-time cosmological evolution. We find solutions which mimic many of the phenomenological features seen in the post-inflation Universe. The effects due to non-minimal scalar couplings to matter are also shown to be negligible in this context. Such solutions can be shown to be stable under homogeneous perturbations. Some restrictions on the value of the slope of the scalar coupling to the Gauss-Bonnet term are found to be necessary to avoid late-time superluminal behaviour and dominant energy condition violation. A number of observational tests are carried out in chapter five on a new approach to averaging the inhomogeneous Universe. In this "Fractal Bubble model" cosmic acceleration is realised as an apparent effect, due to quasilocal gravitational energy gradients. We show that a good fit can be found to three separate observations, the type Ia supernovae, the baryon acoustic oscillation scale and the angular scale of the sound horizon at last scattering. The best fit to the supernovae data is χ² ≃ 0:9 per degree of freedom, with a Hubble parameter at the present epoch of H0 = 61:7+1:4 -1:3 km sec⁻¹ Mpc⁻¹ , and a present epoch volume void fraction of 0:76 ± 0:05