Mathematics – Logic
Scientific paper
Apr 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008phdt.......425s&link_type=abstract
Academic Dissertation for the Degree of Doctor of Philosophy, pp. i-iv, 1-86, April 2008, 86 pages
Mathematics
Logic
Scientific paper
This thesis considers extended theories of gravity as a possible solution to the dark energy problem and in particular studies the impact of Solar System constraints on scalar-tensor theory and f(R) gravity. The present observational status in cosmology and the basic properties of scalar-tensor theory and f(R) gravity are reviewed. The main work is then presented in four appended papers. In summary, Solar System observations put strong constraints on both scalartensor theory and f(R) gravity, in particular via the post-Newtonian parameter γPPN which is the main focus of this thesis. The scalar-tensor theory discussed in the first paper is a model inspired by large extra dimensions. Here, two large extra dimensions offer a possible solution to the hierarchy problem and the effective four-dimensional theory is a dilatonic scalar-tensor theory exhibiting a cosmological behaviour similar to quintessence. It was shown that this model can also give rise to other types of cosmologies, some more akin to k-essence and possibly variants of phantom dark energy. The observational limits on γPPN strongly constrain the scalar field coupling to matter, which together with the cosmological constraints nearly determine the model parameters. The work presented in the three latter papers considered static, spherically symmetric spacetimes in f(R) gravity. The generalized Tolman-Oppenheimer- Volkoff equations were derived both in the metric and in the Palatini formalism of f(R) gravity. By solving these equations for the configuration corresponding to the Sun, it was shown that metric f(R) gravity will in general fail the strong constraint on γPPN, whereas Palatini f(R) gravity will yield the observed value, γPPN ≈ 1. However, the non-standard relation between the gravitational mass and the density profile of a star in f(R) gravity will constrain the allowed forms of the function f(R) also in the Palatini formalism. Although solutions corresponding to γPPN ≈ 1 do exist in the metric formalism, a study of the stability properties of the spherically symmetric solutions reveals a necessity for extreme fine tuning, which affects all presently known metric f(R) models in the literature.
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