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Cosmological inflation and large-scale structure. (English) Zbl 0952.83001

Cambridge: Cambridge University Press. 430 p. (1999).
Lyth and Liddle are two well-known researchers in cosmology. Now they wrote a 400-pages book on Cosmological inflation and large-scale structure, which represents a carefully collected overview about this quickly developing subject.
The two topics mentioned in the title are closely related because now it is generally accepted that the large-scale structure of the Universe (i.e., how the galaxies are distributed) has its origin in the inflationary phase of cosmic evolution, i.e. that period where the Universe expanded quicker than linearly in time.
From the many possibilities to get an inflationary Universe model, the authors concentrate on scalar-field generated models. However, the first inflationary model was introduced without a scalar field by Starobinsky in 1980 as a property of the gravitational sector where one-loop quantum corrections to the Einstein-Hilbert actions have been added, see page 228.
Since then, the models have been refined in many respects, and the authors of the book carefully compare all these models, and how they are related to possible observations. The latter are: The anisotropy of the cosmic background radiation and the large-scale distribution of the galaxies.
From the mathematical point of view the most advanced topic of this book is chapter 14, where the time-evolution of small inhomogeneities within general relativity theory has been carefully deduced for spacetimes usually considered in inflationary cosmology.
This book really fills a gap, and it is highly recommended both for students and researchers in cosmology.

MSC:

83-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory
83F05 Relativistic cosmology
83B05 Observational and experimental questions in relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
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