Structures in the Universe by Exact Methods: Formation, Evolutions, Interactions (Cambridge Monographs on MathematicalPhysics)

Abstract

In this book the use of inhomogeneous models in cosmology, both inmodelling structure formation and interpreting cosmologicalobservations, is discussed. The authors concentrate on exactsolutions, and particularly the Lemaitre–Tolman (LT) and Szekeresmodels (the important topic of averaging is not discussed). The bookserves to demonstrate that inhomogeneous metrics can generaterealistic models of cosmic structure formation and nonlinearevolution and shows that general relativity has a lot more to offerto 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 thebook) a reasonable discussion of the potential problems with thestandard FLRW cosmology is presented, and a list of examplesillustrating the limitations of standard FLRW cosmology are discussed(including potential problems with perturbation methods). Inparticular, the authors argue that the assumptions of isotropy andspatial homogeneity (and consequently the Copernican principle) mustbe properly challenged and revisited. Indeed, it is possible for`good old general relativity' to be used to explain cosmologicalobservations without introducing speculative elements.In part I of the book the necessary background is presented (readersneed a background in general relativity theory at an advancedundergraduate 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 Szekeresmodels. Light propogation (i.e. null geodesics, for both central andoff-center observers) in exact inhomogeneous (LT) models is reviewed.In part II a number of applications of exact inhomogeneous models arepresented (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 structureformation. I thought that the authors describe the advantages anddrawbacks of the idealized exact solutions used in the physicalmodelling in a reasonable manner (although more concise conclusionsmight have been useful). The authors also address the formation of agalaxy with a central black hole, the formation and evolution of richgalactic clusters and voids and other structures, and the effects ofradiation in the models.The most interesting application is presented in chapter 5; namely,the effects of inhomogeneities on observations such as the luminositydistance relation and the explanation of the observed dimming ofdistant SN Ia (which is usually interpreted within the standard FLRWmodel in terms of the existence of dark energy). The main conclusionof this work is that data can be reproduced within the LT model (viainhomogeneities in general relativity, but without introducing darkenergy). In particular, a number of exact LT solutions weresurveyed, 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 problemwithout inflation, in terms of shell crossing in a LT model, isdiscussed. This is perhaps the most controversial chapter of thebook. In the final chapter 7, the influence of inhomogeneousstructures in the path of a light ray (for both center and off-centerobservers in a special Szekeres Swiss cheese model) on the observedtemperature distribution of the CMB is discussed. This is a veryimportant topic, but only a heuristic and qualitative study ispresented here; more work on the multipole moments of higher orderwould be necessary for a more comprehensive analysis.