By V. A. Rubakov D. S. Gorbunov
This publication accompanies one other booklet through an identical authors, creation to the speculation of the Early Universe: scorching large Bang thought and offers the speculation of the evolution of density perturbations and relic gravity waves, idea of cosmological inflation and post-inflationary reheating. Written in a pedagogical type, the most chapters provide a close account of the validated thought, with derivation of formulation. Being self-contained, it's a precious textbook for complex undergraduate scholars and graduate scholars. crucial fabrics from normal Relativity, conception of Gaussian random fields and quantum box concept are accumulated within the appendices. The extra complicated issues are approached equally in a pedagogical approach. those elements may possibly function an in depth creation to present examine.
to be had as a collection with creation to the speculation of the Early Universe: scorching titanic Bang thought.
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Extra resources for Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory
42) Let us discuss these properties in more detail. Let the unit vectors e(1 ) and e (2) be orthogonal to each other and to vector k and form , together with k , right-handed triple (analogous to vectors ix, i y , iz of t he standard orthogonal coordinate frame in 3-dimensional Euclidean space) . Then t he rotation by angle a around the vector k gives eO )1 = e (l) e (2)1 = e (2) cos a cos a e (2) sin a + e (l) sin a. 5 . 2. E 25 ceo the vectors ~ ,ansform as follows T his precisely means that the vector e ( +) belongs to t he irreducible representation of 50(2) of helicity + 1, while helicity of e (- ) is - 1.
K2 = O(m) . We again set u = O(m - 1 ), w = O(m - 2 ) , = O (mO). Then Eq. 74) requires that , formally, 6p = O(m ). 104), i. 122) Then the energy density perturbation is, to the leading order , i5p'P = m 2 uA , (2. 112 ). However, the expression in the right hand side is no longer equal to zero. 96) now gives two equations B' 3a k2 - + - ' B + mau + - - A = 2a 2ma A' + 3a' A 2a - O. ' ~ B = O. 112) into the form _ i5p'P = k2 - 2 uA. 4a This expression is of order O (m O) . Hence, generally speaking , pressure is no longer negligible.
4 1) gives a' o7)[(p + p)V'yl + 4- (p + p)V,y = O. 65) , see problem E. g. 65) contains the sum of contributions of all components. This point is actually not very relevant here: since Wr does not enter Eq. 64), velocity ~T can be found for each of the components in terms of t he initial velocity, and then Wr can be found from Eq. 65 ) as a sum of contributions of all components. Note t hat t he general solution to Eq. 34)). Thus, no non-vanishing solutions to Eq. 65) exist in t he absence of matter.