# Cosmology and Particle Astrophysics (Springer Praxis Books / by Lars Bergström, Ariel Goobar

By Lars Bergström, Ariel Goobar

Beginning with a few simple proof concerning the observable universe the authors think of in successive chapters the total variety of subject matters that make up a level direction in cosmology and particle astrophysics. the exceptional characteristic of this publication is that it truly is self-contained, in that no specialized wisdom is needed at the a part of the reader, except easy undergraduate arithmetic and physics.

This paperback version will back objective scholars of physics, astrophysics and cosmology on the complex undergraduate point or early graduate point. one of many book’s greatest robust issues is that the authors quickly contain scholars within the most enjoyable of cutting-edge advancements within the box in an easy and self-contained demeanour, relegating the extra technical facets to appendices. The labored examples through the ebook, and summaries on the finish of every bankruptcy, which have been improved within the moment version, were rather well got by way of students.

This ebook bargains complicated undergraduate point and starting graduate point scholars a hugely readable, but accomplished evaluate of particle astrophysics. Competing books disguise this subject at too complex a degree for this readership.

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**Example text**

A light-ray arriving at the common origin at time t = t = 0 in two inertial frames. The primed frame is moving with velocity v with respect to the unprimed frame, and the measured angles of incidence are θ and θ, respectively. We ﬁrst derive the transformation properties of velocities (that is, the addition law for relativistic velocities). 18). 62) It is interesting to note the factor 1/γ(v) which enters the expression for sin θ . 61) is unchanged. It means that, for instance, light-rays which are either incident or emitted isotropically in one system are driven to small angles in a moving frame.

B) The circumference and radius of a circle drawn out on a saddle surface have a ratio greater than 2π. Answer: Let the circle subtend a half-angle of θ = s/a (see Fig. 5 (a)). Then the circumference of the circle is c = 2πr = 2πa sin θ ≈ 2πa Thus, the curvature K is ⎛ 2πs − 2πs 1 − 3 K = lim ⎝ π s→0 s3 s 1 s3 − + ... a 6 a3 s2 6a2 = 2πs 1 − s2 + ... 6a2 ⎞ ⎠= 1 a2 We may introduce coordinates (r , φ) on the sphere with the property (see Fig. 5 (a)) that the circumference of a circle around the North Pole has the value exactly equal to 2πr .

As β → 1 this diverges, which shows that a massive particle can never attain the speed of light, since it would cost inﬁnite energy to accelerate it to that speed. The variation of γ with β, or rather 1 − β, is shown in Fig. 3. 10 γ(v/c) 10 10 10 10 5 4 3 2 1 0 10 -12 10 -10 10 -8 10 10 -6 -4 10 -2 10 0 10 1-v/c Fig. 3. The dependence of the relativistic gamma factor γ(β), where β = v/c, on the velocity v. The quantity on the horizontal axis is 1 − β = 1 − v/c. As can be seen, in a logarithmic scale the dependence is close to being a straight line except for β close to zero.