A Back-reaction Approach to Dark Energy

3 A " homogeneous " LTB model 29 3. C Sewing the photon path 109 Acknowledgments 111 Bibliography 113 vi CONTENTS Introduction This thesis is mainly about how to set up and carry out the idea of back-reaction in a physically meaningful way. Most, if not all, observations are consistent with the cosmic concordance model according to which, today, one-fourth of the mass-energy of the universe is clustered and dominated by cold dark matter. The remaining three-quarters is uniform and dominated by a fluid with a negative pressure (dark energy, or Λ). While the standard ΛCDM model seems capable of accounting for the observations , it does have the feature that approximately 95% of the mass-energy of the present universe is unknown. We are either presented with the opportunity of discovering the nature of dark matter and dark energy, or nature might be different than described by the ΛCDM model. Regardless, until such time as dark matter and dark energy are completely understood, it is useful to look for alternative cosmological models that fit the data. One non-standard possibility is that there are large effects on the observed expansion rate (and hence on other observables) due to the back-reaction of inho-mogeneities in the universe. The basic idea is that all evidence for dark energy comes from the observational determinations of the expansion history of the universe. Anything that affects the observed expansion history of the universe alters the determination of the parameters of dark energy; in the extreme it may remove the need for dark energy. The " safe " consequence of the success of the concordance model is that the isotropic and homogeneous ΛCDM model is a good phenomenological fit to the real inhomogeneous universe. And this is, in some sense, a verification of the cosmological principle: the inhomogeneous universe can be described by means of an isotropic and vii viii INTRODUCTION homogeneous solution. However, this does not imply that a primary source of dark energy exists, but only that it exists as far as the phenomenological fit is concerned. For example, it is not straightforward that the universe is accelerating. If dark energy does not exist at a fundamental level, its presence in the concordance model would tell us that the pure-matter inhomogeneous model has been renormalized, from the phenomenological point of view (luminosity-distance and redshift of photons), into a homogeneous ΛCDM model. There are two ways to …