Ebook Physical foundations of cosmology: Part 2
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Ebook Physical foundations of cosmology: Part 2
5Inflation I: homogeneous limitMatter is distributed very homogeneously and isotropically on scales larger than a few hundred megaparsecs. The CMB giv Ebook Physical foundations of cosmology: Part 2ves US a “photograph” of the early universe, which shows that al recombination the universe was extremely homogeneous and isotropic (with accuracy — 10 4) on all scales up to the present horizon. Given that the universe evolves according to the Hubble law. it is natural to ask which initial conditio Ebook Physical foundations of cosmology: Part 2ns could lead to such homogeneity and isotropy.To obtain an exhaustive answer to this question we have to know the exact physical laws which govern thEbook Physical foundations of cosmology: Part 2
e evolution of the very early universe. However, as long as we are interested only in the general features of the initial conditions it suffices to kn5Inflation I: homogeneous limitMatter is distributed very homogeneously and isotropically on scales larger than a few hundred megaparsecs. The CMB giv Ebook Physical foundations of cosmology: Part 2eral Relativity (sec Part II of this book for details). We will also assume that nonperturbative quantum gravity does not play an essential role at sub-Planckian curvatures. On the other hand, we are nearly certain that nonperlurbalivc quantum gravity effects become very important when the curvature Ebook Physical foundations of cosmology: Part 2 reaches Planckian values and the notion of classical spacetime breaks down. Therefore we address the initial conditions at the Planckian time lị = IEbook Physical foundations of cosmology: Part 2
PI IO-43 s.In this chapter we discuss the initial conditions problem we face in a decelerating universe and show how this problem can be solved if the5Inflation I: homogeneous limitMatter is distributed very homogeneously and isotropically on scales larger than a few hundred megaparsecs. The CMB giv Ebook Physical foundations of cosmology: Part 2 conditions characterizing matter: (a) its spatial distribution, described by the energy density s(x) and (b) the initial field of velocities. Let US determine them given the current state of the universe.Homogeneity, isotropy (horizon) problem The present homogeneous, isotropic do-5. / Problem of i Ebook Physical foundations of cosmology: Part 2nitial conditionsInitially the size of this domain was smaller by the ratio of the corresponding scale factors, a,/an. Assuming that inhomogeneity canEbook Physical foundations of cosmology: Part 2
not be dissolved by expansion, we may safely conclude that the size of the homogeneous, isotropic region from which our universe originated at t = tị 5Inflation I: homogeneous limitMatter is distributed very homogeneously and isotropically on scales larger than a few hundred megaparsecs. The CMB giv Ebook Physical foundations of cosmology: Part 2f this ratio we note that if the primordial radiation dominates at tị ~ fp/, then its temperature is Tpi ~ IO'2 K. Hence(a, Ị (lị)) ~ (Tị)/ Tpi)10 22and we obtainh IO17,102 •-5.3lc 10 43Thus, al the initial Planckian lime, the size of our universe exceeded the causality scale by 28 orders of magnitu Ebook Physical foundations of cosmology: Part 2de. This means that in 10s4 can sally disconnected regions the energy density was smoothly distributed with a fractional variation not exceeding $$/£Ebook Physical foundations of cosmology: Part 2
— 10 4. Because no signals can propagate faster than light, no causal physical processes can be responsible for such an unnaturally line-tuned matter 5Inflation I: homogeneous limitMatter is distributed very homogeneously and isotropically on scales larger than a few hundred megaparsecs. The CMB giv Ebook Physical foundations of cosmology: Part 2e was initially larger than that of a causal patch by the ratio of the corresponding expansion rates. Assuming that gravity was always attractive and hence was decelerating the expansion, we conclude from (5.4) that the homogeneity scale was always larger than the scale of causality. Therefore, the Ebook Physical foundations of cosmology: Part 2homogeneity problem is also sometimes called the horizon problem.Initial velocities (flatness) problem Let us suppose for a minute that someone has maEbook Physical foundations of cosmology: Part 2
naged to distribute matter in the required way. The next question concerns initial velocities. Only after they are specified is the Cauchy problem com5Inflation I: homogeneous limitMatter is distributed very homogeneously and isotropically on scales larger than a few hundred megaparsecs. The CMB giv Ebook Physical foundations of cosmology: Part 2 law because otherwise228Inflation Ỉ: homogeneous limitcausally disconnected regions further complicates the horizon problem. Assuming that it has. nevertheless, been achieved, we can ask how accurately the initial Hubble velocities have to be chosen for a given matter distribution.Let us consider a Ebook Physical foundations of cosmology: Part 2 large spherically symmetric cloud of matter and compare its total energy with the kinetic energy due to Hubble expansion, Ek. rhe total energy is theEbook Physical foundations of cosmology: Part 2
sum of the positive kinetic energy and the negative potential energy of the gravitational self-interaction. Ep. It is conserved: c7E'°' = Eỉ + E!' = 5Inflation I: homogeneous limitMatter is distributed very homogeneously and isotropically on scales larger than a few hundred megaparsecs. The CMB giv Ebook Physical foundations of cosmology: Part 2ce Efr ~ I Efi\ and àty/ài < 10 28, we findt;tot5Inflation I: homogeneous limitMatter is distributed very homogeneously and isotropically on scales larger than a few hundred megaparsecs. The CMB givGọi ngay
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