By Dmitry S. Gorbunov
ISBN-10: 9814322245
ISBN-13: 9789814322249
ISBN-10: 9814343978
ISBN-13: 9789814343978
This publication is written from the point of view of a deep connection among cosmology and particle physics. It offers the implications and concepts on either the homogeneous and isotropic Universe on the scorching degree of its evolution and in later levels. the most chapters describe in a scientific and pedagogical method confirmed proof and ideas at the early and the current Universe. the excellent remedy, therefore, serves as a latest advent to this speedily constructing box of technology. to aid in analyzing the chapters with no need to continually seek advice different texts, crucial fabrics from basic Relativity and the idea of simple debris are accumulated within the appendices. quite a few hypotheses facing unsolved difficulties of cosmology, and sometimes substitute to one another, are mentioned at a extra complicated point. those trouble darkish subject, darkish strength, matter-antimatter asymmetry, and so on.
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Additional resources for Introduction to the Theory of the Early Universe: Hot Big Bang Theory
Example text
40). 39). 17). Thus, spatial components of Eq. 39) (μ = i = 1, 2, 3) read dui + Γi0j u0 uj + Γij0 uj u0 = 0, ds or dui a˙ dt i +2 u = 0. ds a ds In terms of the physical components the latter equation is a˙ dU i = − U i. 38) is indeed valid. Thus, the velocities of free particles with respect to comoving frame decrease in expanding Universe; particles gradually “freeze in”. In particular, if at early cosmological stages massive particles were relativistic, they become non-relativistic at later stages.
6) One of the properties of homogeneous and isotropic spaces is that all covariant geometrical quantities are expressed through the metric tensor γij and, possibly, tensors δij and Eijk , the latter existing in any Riemannian space, see Appendix A (here i, j = 1, 2, 3; we denote the metric tensor of 3-dimensional space by γij to distinguish it from the metric tensor gμν of 4-dimensional space-time). Furthermore, the coefficients do not depend on coordinates. 1. 7) that the Ricci tensor is κ (3) Rij = 2 2 γij , R and the curvature scalar is constant in space and equal to 6κR−2 .
In analogy to 3-sphere, 3-dimensional hyperboloid is conveniently described by its embedding into fictitious 4-dimensional Minkowski space with metric ds2 = −(dy 1 )2 + (dy 2 )2 + (dy 3 )2 + (dy 4 )2 , while the equation for the hyperboloid is (y 1 )2 − (y 2 )2 − (y 3 )2 − (y 4 )2 = R2 . 4) We are interested in the one connected component y 1 > 0. 1. Show that the hyperboloid is indeed a homogeneous and isotropic space. Hint: Begin with defining what precisely is a homogeneous and isotropic space.
Introduction to the Theory of the Early Universe: Hot Big Bang Theory by Dmitry S. Gorbunov
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