Mathematics – Logic
Scientific paper
Nov 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008cqgra..25v9003.&link_type=abstract
Classical and Quantum Gravity, Volume 25, Issue 22, pp. 229003 (2008).
Mathematics
Logic
Scientific paper
The field of cosmology has been transformed since the glorious decades of the 1920's and 1930's when theory and observation converged to develop the current model of the expanding universe. It was a triumph of the theory of general relativity and astronomy. The first revolution came when the nuclear physicists entered the fray. This marked the debut of the hot big bang, in which the light elements were synthesized in the first three minutes. It was soon realised that elements like carbon and iron were synthesized in exploding stars. However helium, as well as deuterium and lithium, remain as George Gamow envisaged, the detritus of the big bang. The climax arrived with one of the most remarkable discoveries of the twentieth century, the cosmic microwave background radiation, in 1964. The fossil glow turned out to have the spectrum of an ideal black body. One could not imagine a stronger confirmation of the hot and dense origin of the universe.
This discovery set the scene for the next major advance. It was now the turn of the particle physicists, who realized that the energies attained near the beginning of the universe, and unachievable in any conceivable terrestrial accelerator, provided a unique testing ground for theories of grand unification of the fundamental forces. This led Alan Guth and Andrei Linde in 1980 to propose the theory of inflation, which solved outstanding puzzles of the big bang. One could now understand why the universe is so large and homogeneous, and the origin of the seed fluctuations that gave rise to large-scale structure. A key prediction was that the universe should have Euclidean geometry, now verified to a precision of a few percent.
Modern cosmology is firmly embedded in particle physics. It merits a text written by a particle physicist who can however appreciate the contributions of astronomy that provide the foundation and infrastructure for the theory of the expanding universe. There are now several such texts available. The most recent, and comprehensive, is Cosmology, in which the University of Texas physicist and Nobel Laureate, Steven Weinberg provides a concise introduction to modern cosmology. The book is aimed at the level of a final year physics undergraduate, or a first year graduate student. The discussion is self-contained, with numerous derivations. It begins with an overview of the standard cosmological model, and presents a detailed treatment of fluctuation growth. There are sections on gravitational lensing and inflationary cosmology, on microwave background fluctuations and structure growth.
There are aspects however where a supplementary book is essential for the physicist being introduced to cosmology. The text is lacking in physical cosmology. The baryon physics of galaxy formation is barely mentioned, apart from a discussion of the Jeans mass. And it ignores one of the greatest contributions to the field by Russian cosmologist Yaakov Zel'dovich, who discovered the only nonspherical solution to the nonlinear evolution of density fluctuations, one that has since dominated our understanding of the large-scale structure of the universe via the cosmic web. But these are minor quibbles about what provides an outstanding introduction to modern cosmology, and one that takes us from the physics fundamentals up to the cosmic frontier.
I recommend Cosmology for anyone wishing to enter the field and with a good physics background. It is ideal for the astronomer who may only have a sketchy knowledge of general relativity or particle physics. She will learn about vielbeins and scalar fields, gauge-invariant fluctuation theory and inflation. Steven Weinberg is a leading physicist who has also made important contributions to cosmology. The text provides a rigorous treatment of the standard model of cosmology, and of structure formation. Numerous exercises are provided. It provides an excellent core for a course on cosmology.
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