Alternative Theories of Gravity

ACKNOWLEDGEMENTS This work would not have been possible without the help of a lot of people. I would like to thank my family and friends for their encouragement, my collaborators David Mota and Robert Scherrer for their hard work and my office mate Simon West for innumerable delightful lunches. Most of all I would like to thank my supervisor, John Barrow, for his constant support, his guidance and for his untiring correction of my speling and, grammar. i DECLARATION The research presented in this thesis was performed in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge between October 2003 and July 2006. This dissertation is the result of my own work, except as stated below or where explicit reference is made to the results of others. A brief discussion of the number of arbitrary functions in section 5.2.1 is due to John Barrow. Section 5.2.3 was written collaboratively with John Barrow where the analysis of R n theories in this section is due primarily to him. Discussion in the introduction to section 7.1 is also due to John Barrow. Section 7.1.3 was written collaboratively with David Mota where his main contribution was the numerical calculations involved and the production and discussion of figures 7.6 to 7.15. In section 9.1.1 the numerical work and the production of figure 9.1 was performed by Robert Scherrer. John Barrow also provided ideas and guidance which were of use throughout this work. Use was made of the computer programs Mathematica and Maple. This dissertation is not substantially the same as any that I have submitted, or am submitting, for a degree, diploma or other qualification at any other university. SUMMARY This work investigates alternative theories of gravity, the solutions to their field equations and the constraints that can be imposed upon them from observation and experiment. Specifically, we consider the cosmologies and spherically symmetric solutions that can be expected to result from scalar-tensor and fourth-order theories of gravity. We find exact cosmological solutions of various different kinds; isotropic and anisotropic, homogeneous and inhomogeneous. These solutions are used to investigate the behaviour of the Universes at both late and early times, to investigate the effects of corrections to general relativity on approach to an initial singularity and to look for effects which may be observable in the present day Universe. We use physical processes, such as the primordial nucleosynthesis of the …