By J. N. Islam

ISBN-10: 0521496500

ISBN-13: 9780521496506

This e-book offers a concise creation to the mathematical facets of the beginning, constitution and evolution of the universe. The e-book starts with a quick evaluation of observational and theoretical cosmology, besides a quick advent of common relativity. It then is going directly to speak about Friedmann types, the Hubble consistent and deceleration parameter, singularities, the early universe, inflation, quantum cosmology and the far-off way forward for the universe. This re-creation features a rigorous derivation of the Robertson-Walker metric. It additionally discusses the boundaries to the parameter area via a variety of theoretical and observational constraints, and offers a brand new inflationary answer for a 6th measure strength. This e-book is acceptable as a textbook for complex undergraduates and starting graduate scholars. it's going to even be of curiosity to cosmologists, astrophysicists, utilized mathematicians and mathematical physicists.

Show description

Read Online or Download An Introduction to Mathematical Cosmology PDF

Best cosmology books

Download PDF by Stephen W. Hawking, Ron Miller, Carl Sagan: A Brief History of Time: From the Big Bang to Black Holes

Stephen Hawking, essentially the most amazing theoretical physicists in heritage, wrote the fashionable vintage a short background of Time to aid nonscientists comprehend the questions being requested through scientists this day: the place did the universe come from? How and why did it start? Will it come to an finish, and if that is so, how?

Derek Raine, E.G. Thomas's An Introduction to the Science of Cosmology PDF

An intensive creation to trendy principles on cosmology and at the actual foundation of the overall conception of relativity, An creation to the technological know-how of Cosmology explores numerous theories and ideas in sizeable bang cosmology, supplying perception into present difficulties. Assuming no prior wisdom of astronomy or cosmology, this booklet takes you past introductory texts to the purpose the place you can learn and delight in the medical literature, that's commonly referenced within the e-book.

Download e-book for kindle: The Biggest Bangs: The Mystery of Gamma Ray Bursts, the Most by Jonathan I. Katz

Gamma-ray bursts are the main violent occasions because the delivery of the universe. they're approximately ten occasions extra vigorous than the main robust supernovae. At their top, gamma-ray bursts are the brightest items in area, approximately 100,000 occasions brighter than a complete galaxy. And but till lately those colossal eruptions have been the main mysterious occasions in astronomy.

The B−L Phase Transition: Implications for Cosmology and by Kai Schmitz PDF

Numerous of the very foundations of the cosmological normal version — the baryon asymmetry of the universe, darkish topic, and the beginning of the new massive bang itself — nonetheless demand an evidence from the point of view of primary physics. This paintings advocates one exciting risk for a constant cosmology that fills within the theoretical gaps whereas being absolutely in line with the observational facts.

Additional resources for An Introduction to Mathematical Cosmology

Sample text

32), the ‘radius’ of this sphere, that is, the distance from the ‘centre’ given by ␺ ϭ0 to the surface given by ␺ ϭ ␺0 along ␪ ϭ constant and ␾ ϭconstant, is R␺0. Thus the surface area is larger than that of a sphere of radius R␺0 in Euclidean space. In this case the range of the coordinates (␺, ␪, ␾) is: 0ഛ ␺ ഛϱ,0ഛ ␪ ഛ ␲, 0ഛ ␾ Ͻ 2␲. The spatial volume is infinite. 3 Some kinematic properties of the Robertson–Walker metric We have seen that galaxies have fixed spatial coordinates, that is, they are at rest in the coordinate system defined above.

66) Again making use of expansion of determinants one can show that ␧␣␤␥␦ ϭ(Ϫ )␧␣␤␥␦. 67) It can be verified that ␧␣␤␥␦ is a covariant tensor density of weight Ϫ1. The Levi–Civita tensor density is used for defining the ‘dual’ of antisymmetric tensors, such as that of the electromagnetic field tensor F␮␯, the Yang–Mills field tensor, or, with respect to suitable indices, of the Riemann tensor (the latter are needed for some of the so-called ‘curvature invariants’, which will be mentioned later in connection with singularities).

1) does not incorporate the property that space is homogeneous and isotropic. This form of the metric can be used, with the help of a special coordinate system obtained by singling out a particular typical galaxy, to derive some general properties of the universe without the assumptions of homogeneity and isotropy (see, for example, Raychaudhuri (1955)). 1) when space is homogeneous and isotropic. The spatial separation on the same hypersurface t ϭconstant of two nearby galaxies at coordinates (x1, x2, x3) and (x1 ϩ⌬x1, x2 ϩ⌬x2, x3 ϩ⌬x3) is d␴2 ϭhij ⌬xi⌬xj.

Download PDF sample

An Introduction to Mathematical Cosmology by J. N. Islam


by Brian
4.4

An Introduction to Mathematical Cosmology by J. N. Islam PDF
Rated 4.57 of 5 – based on 27 votes