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Nonlinear Backreaction in Cosmology

出版	University of Chicago, Division of the Physical Sciences, Department of Physics, 2012
ISBN	12676037639781267603760
URL	http://books.google.com.hk/books?id=A-ARngEACAAJ&hl=&source=gbs_api

註釋This thesis, based on two papers by Green and Wald, investigates the problem of nonlinear backreaction in cosmology. We first analyze the problem in a general context by developing a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our framework requires the metric to be close to a background metric (not necessarily a cosmological metric), but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e., positivity of energy density in all frames), then the only effect that small-scale inhomogeneities can have on the background metric is to provide an effective stress-energy tensor that is traceless and satisfies the weak energy condition itself & mdash;corresponding to the presence of gravitational radiation. In particular, nonlinear effects produced by small-scale inhomogeneities cannot mimic the effects of dark energy. We also develop perturbation theory off of the background metric. We derive an equation for the long-wavelength part of the leading order deviation of the metric from the background metric, which contains the usual terms occurring in linearized perturbation theory plus additional contributions from the small-scale inhomogeneities. Next, we apply our framework to the cosmological context, specializing our background metric to be of the Friedmann-Lemaitre-Robertson-Walker form. We demonstrate that, in the case of dust matter, a cosmological constant, and vanishing spatial curvature (i.e., our universe today), Newtonian gravity alone provides a good global description of an inhomogeneous general relativistic cosmology, even when there is significant nonlinear dynamical behavior at small scales. Namely, we find a relatively straightforward dictionary & mdash;which is exact at the linearized level & mdash;that maps Newtonian dust cosmologies into general relativistic dust cosmologies. We show that, under this dictionary, Einstein's equation is satisfied to a high degree of accuracy within an "ordering scheme'' which is motivated by our general framework. At large scales, this approximate solution satisfies the long-wavelength perturbation equation derived in the general context. We find that the dominant contributions from small-scale inhomogeneities correspond precisely to kinetic energy and Newtonian binding energy, and can be interpreted as slightly perturbing the background dust energy density. This latter part not only illustrates the applicability of our general framework, but it also provides strong justification for the use of Newtonian N-body simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.