Mathematics – Logic
Scientific paper
May 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cqgra..27j9002c&link_type=abstract
Classical and Quantum Gravity, Volume 27, Issue 10, pp. 109002 (2010).
Mathematics
Logic
Scientific paper
In this book the use of inhomogeneous models in cosmology, both in modelling structure formation and interpreting cosmological observations, is discussed. The authors concentrate on exact solutions, and particularly the Lemaitre-Tolman (LT) and Szekeres models (the important topic of averaging is not discussed). The book serves to demonstrate that inhomogeneous metrics can generate realistic models of cosmic structure formation and nonlinear evolution and shows that general relativity has a lot more to offer to cosmology than just the standard spatially homogeneous FLRW model. I would recommend this book to people working in theoretical cosmology.
In the introduction (and in the concluding chapter and throughout the book) a reasonable discussion of the potential problems with the standard FLRW cosmology is presented, and a list of examples illustrating the limitations of standard FLRW cosmology are discussed (including potential problems with perturbation methods). In particular, the authors argue that the assumptions of isotropy and spatial homogeneity (and consequently the Copernican principle) must be properly challenged and revisited. Indeed, it is possible for `good old general relativity' to be used to explain cosmological observations without introducing speculative elements.
In part I of the book the necessary background is presented (readers need a background in general relativity theory at an advanced undergraduate or graduate level). There is a good (and easy to read) review of the exact spherically symmetric dust Lemaitre-Tolman model (LT) (often denoted the LTB model) and the Lemaitre and Szekeres models. Light propogation (i.e. null geodesics, for both central and off-center observers) in exact inhomogeneous (LT) models is reviewed.
In part II a number of applications of exact inhomogeneous models are presented (taken mainly from the authors' own work). In chapter 4, the evolution of exact inhomogeneous models (primarily the LT model, but also the Szekeres model) is studied regarding structure formation. I thought that the authors describe the advantages and drawbacks of the idealized exact solutions used in the physical modelling in a reasonable manner (although more concise conclusions might have been useful). The authors also address the formation of a galaxy with a central black hole, the formation and evolution of rich galactic clusters and voids and other structures, and the effects of radiation in the models.
The most interesting application is presented in chapter 5; namely, the effects of inhomogeneities on observations such as the luminosity distance relation and the explanation of the observed dimming of distant SN Ia (which is usually interpreted within the standard FLRW model in terms of the existence of dark energy). The main conclusion of this work is that data can be reproduced within the LT model (via inhomogeneities in general relativity, but without introducing dark energy). In particular, a number of exact LT solutions were surveyed, and a full discussion of various models in the literature (and a critique of the various assumptions) is presented.
In the next chapter the possible resolution of the horizon problem without inflation, in terms of shell crossing in a LT model, is discussed. This is perhaps the most controversial chapter of the book. In the final chapter 7, the influence of inhomogeneous structures in the path of a light ray (for both center and off-center observers in a special Szekeres Swiss cheese model) on the observed temperature distribution of the CMB is discussed. This is a very important topic, but only a heuristic and qualitative study is presented here; more work on the multipole moments of higher order would be necessary for a more comprehensive analysis.
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