By J. N. Islam
This e-book presents a concise advent to the mathematical elements of the foundation, constitution and evolution of the universe. The publication starts with a short assessment of observational and theoretical cosmology, in addition to a quick advent of basic relativity. It then is going directly to talk about Friedmann versions, 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 incorporates a rigorous derivation of the Robertson-Walker metric. It additionally discusses the bounds to the parameter house via a number of theoretical and observational constraints, and provides a brand new inflationary answer for a 6th measure strength. This publication is acceptable as a textbook for complicated undergraduates and starting graduate scholars. it is going to even be of curiosity to cosmologists, astrophysicists, utilized mathematicians and mathematical physicists.
Read or Download An introduction to mathematical cosmology PDF
Similar cosmology books
Rupert Sheldrake, one of many world's preeminent biologists, has revolutionized clinical pondering along with his imaginative and prescient of a dwelling, constructing universe--one with its personal inherent reminiscence. within the Rebirth of Nature, Sheldrake urges us to maneuver past the centuries-old mechanistic view of nature, explaining why we will be able to now not regard the realm as inanimate and purposeless.
J. Richard Gott used to be one of the first cosmologists to suggest that the constitution of our universe is sort of a sponge made of clusters of galaxies intricately attached by means of filaments of galaxies--a incredible constitution now known as the "cosmic web" and mapped commonly through groups of astronomers.
For Christians, the problems raised through different perspectives on construction and evolution are difficult. Can a "young earth" be reconciled with a universe that looks to be billions of years outdated? Does medical facts aspect to a God who designed the universe and existence in all its complexity? 3 perspectives on construction and Evolution bargains with those and related matters because it seems to be at 3 dominant faculties of Christian proposal.
- Spin in gravity
- General relativity and gravitation Vol. 10
- Comets: Nature, Dynamics, Origin, and their Cosmogonical Relevance (Astrophysics and Space Science Library, Volume 328)
- Improbable Journeys, 1st Edition
- Classical Measurements in Curved Space-Times (Cambridge Monographs on Mathematical Physics)
- The Privileged Planet: How Our Place in the Cosmos Is Designed for Discovery
Extra info for An introduction to mathematical cosmology
7) it follows that the ﬁrst derivatives of the metric tensor also vanish at this point. This is one form of the equivalence principle, according to which the gravitational ﬁeld can be ‘transformed away’ at any point by choosing a suitable frame of reference. 11) where x0 ϭct, t being the time and (x1, x2, x3) being Cartesian coordinates. 12) is the Riemann tensor deﬁned by where R ϭ⌫ Ϫ⌫ ϩ⌫ ⌫␣ Ϫ⌫ ⌫␣ . 14c) and satisﬁes the Bianchi identity: R ϩR ϩR ϭ0. 15) The Ricci tensor R is deﬁned by R ϭ R ϭR .
43) and so is a Killing vector. Suppose we have only n linearly independent Killing vectors (i), i ϭ1, 2, . . , n and no more. Then the commutator of any two of these is a Killing vector and so must be a linear combination of some or all of the n Killing vectors with constant coeﬃcients since there are no other solutions of Killing’s equation. Thus we have the result (i); ( j) Ϫ ( j); (i) ϭ n ͚a kϭ1 ij (k) , k i, jϭ1, . , n. 50) In coordinate independent notation, we can write [ (i), ( j)]ϭ n ͚a kϭ1 ij (k) , k i, jϭ1, .
A space-like three-surface is a surface deﬁned by f(x0,x1,x2,x3)ϭ0 such that f, f, Ͼ0 when fϭ0. The unit normal vector to this surface is given by n ϭ( ␣␤f,␣ f,␤)Ϫ1/2 f,. Given a vector ﬁeld , one can deﬁne a set of curves ﬁlling all space such that the tangent vector to any curve of this set at any point coincides with the value of the vector ﬁeld at that point. This is done by solving the set of ﬁrst order diﬀerential equations. 30) where on the right hand side we have put x for all four components of the coordinates.