By Dmitry S. Gorbunov

This ebook 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 phases. the most chapters describe in a scientific and pedagogical approach verified evidence and ideas at the early and the current Universe. the great remedy, accordingly, serves as a latest creation to this swiftly constructing box of technological know-how. to aid in examining the chapters with no need to continually seek advice different texts, crucial fabrics from common Relativity and the idea of straight forward debris are accrued within the appendices. a variety of hypotheses facing unsolved difficulties of cosmology, and infrequently replacement to one another, are mentioned at a extra complicated point. those main issue darkish subject, darkish strength, matter-antimatter asymmetry, and so forth.

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**Extra resources for Introduction to the Theory of the Early Universe: Hot Big Bang Theory**

**Example text**

Hence, vacuum energy does not cluster, so it is indeed an excellent candidate for dark energy. The problem, though, is that the energy density has dimension M 4 , and one would expect oﬀhand that the value of vacuum energy density would be of the order of the fourth power of the mass scale of fundamental interactions. These scales are 1 GeV for strong interactions, 100 GeV for electroweak interactions and MP l ∼ 1019 GeV for gravitational interactions themselves. 19) Any of these estimates exceeds by many orders of magnitude the actual dark energy density ρΛ ∼ ρc ∼ 10−5 GeV ∼ 10−46 GeV4 .

17 This mechanism does not work for relativistic particles, since weak gravitational ﬁeld cannot keep them inside an overdense region. 7. 7 27 Inﬂationary Epoch The Hot Big Bang theory has its problems. Part of them is due to the fact that this theory needs very special initial conditions, otherwise it would grossly fail to describe the early and present Universe. We discuss the problem of initial conditions in the accompanying book, and here we give one example showing what sort of problems we are talking about.

24) this action has the form S= d3 xdη m2 a4 2 1 2 μν a η ∂μ φ∂ν φ − φ . 2 2 Equation obtained from this action by varying with respect to φ is the Klein–Gordon equation in expanding Universe (in conformal coordinates) 1 ∂η (a2 ∂η φ) − ∂i ∂i φ + m2 a2 φ = 0. 41) 40 Homogeneous Isotropic Universe This equation again does not contain spatial coordinates explicitly, so its solutions are again superpositions of plane waves 1 f (η)e−ikx , a(η) φ= where k is independent of time. 38). 6. Show that for slowly varying scale factor, solutions to Eq.