An Introduction to Mathematical Cosmology by J. N. Islam

By J. N. Islam

This e-book presents a concise advent to the mathematical features of the starting place, constitution and evolution of the universe. The publication starts with a short evaluate of observational and theoretical cosmology, besides a quick creation of basic relativity. It then is going directly to speak about Friedmann versions, the Hubble consistent and deceleration parameter, singularities, the early universe, inflation, quantum cosmology and the far away way forward for the universe. This re-creation includes a rigorous derivation of the Robertson-Walker metric. It additionally discusses the bounds to the parameter area via numerous theoretical and observational constraints, and provides a brand new inflationary resolution for a 6th measure capability. This booklet is appropriate as a textbook for complicated 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

Cosmology

Cosmology bargains with the present country of wondering the elemental questions on the heart of the sphere of cosmology. extra emphasis than traditional is wear the connections to similar domain names of technological know-how, similar to geometry, relativity, thermodynamics, particle physics, and - particularly - at the intrinsic connections among different subject matters.

The Mystery of the Missing Antimatter (Science Essentials)

Within the first fractions of a moment after the large Bang lingers a query on the center of our very lifestyles: why does the universe include topic yet virtually no antimatter? The legislation of physics let us know that equivalent quantities of topic and antimatter have been produced within the early universe--but then, anything unusual occurred.

The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead

A professor of physics explains how he used a mathematical version of the universe to verify the life of God and the chance that each human who ever lived might be resurrected from the lifeless. Reprint. PW.

Black Holes in Higher Dimensions

Black holes are some of the most notable predictions of Einstein's normal relativity. lately, principles in brane-world cosmology, string concept and gauge/gravity duality have stimulated reports of black holes in additional than 4 dimensions, with excellent effects. In larger dimensions, black holes exist with unique shapes and weird dynamics.

Additional resources for An Introduction to Mathematical Cosmology

Sample text

The parameter t can be chosen to measure the proper time along a geodesic. Now introduce spatial coordinates (x1, x2, x3) which are constant along any geodesic. Thus, for each galaxy the coordinates (x1, x2, x3) are constant. 1) where the hij are functions of (t, x1, x2, x3) and as usual repeated indices are to be summed over (Latin indices take values 1, 2, 3). 1) incorporates the properties described above can be seen as follows. Let the worldline of a galaxy be given by x␮(␶), where ␶ is A simple derivation 39 the proper time along the galaxy.

Put ␮ ϭ1, ␯ ϭ2 to get A1;2 ϪA2;1 ϭA1,2 ϪA2,1. 81) 28 Introduction to general relativity where the integral at the end is over the perimeter ѨS of the area S. We will express this in an invariant manner. An element of surface dS␮␯ given by two infinitesimal contravariant vectors ␰ ␮ and ␨ ␮ is given by dS␮␯ ϭ ␰ ␮␨ ␯ Ϫ ␰ ␯␨ ␮. 82) For example, if ␰ ␮ ϭ(0,dx1,0,0), ␨ ␮ ϭ(0,0,dx2,0), then dS12 ϭdx1dx2, dS21 ϭϪdx1dx2, the other components being zero. 81) becomes 1 2 ΎΎ (A␮;␯ ϪA␯;␮)dS␮␯ ϭ surface Ύ A␮dx␮.

These properties are reflected in the tensor (this discussion is taken from Dirac 1975, 1996, p. 113) 34 Introduction to general relativity with T␮␯ giving the density and flux of energy and momentum. The symmetric tensor T␮␯ is the material energy–momentum tensor. 113) we get T␮␯;␯ ϭ(␳u␮u␯);␯ ϭ(␳u␯);␯u␮ ϩ ␳u␯u␮;␯ ϭ ␳u␯u␮;␯. 104), (u␮,␯u␯ ϩ ⌫␮␯␴u␯u␴)ϭ(u␮,␯ ϩ ⌫␮␯␴u␴)u␯ ϭu␮;␯u␯ ϭ0. 22). 23), being obtained from the latter by setting pϭ0. 116). This zero-pressure form of matter is usually referred to as ‘dust’, and arises in various situations including cosmological ones, as we shall see later.

Download PDF sample

Rated 4.67 of 5 – based on 47 votes