Abstract
The cosmological principle is an idealization of what we observe in nature. At late times, matter does not occupy the whole space uniformly due to gravitational clustering. Near the big bang, a homogeneous and isotropic universe is not the most general initial condition. Even if one chose FLRW as the classical initial state at very early times, quantum fluctuations of particle fields would be of the same order of the particle horizon, and they would give rise to strong inhomogeneities in the metric and matter energy density. On the other hand, CMB anisotropies are rather small and a perfect FLRW background is still a good lowest-order approximation. A reasonable hypothesis, verified by experiments, is that CMB anisotropies come from these metric and density perturbations. Because the effect is so small, the formalism of linear perturbations is well suited for our purpose [1–4]. One should also explain why non-linear inhomogeneities [5] do not play a major role in the early universe. We shall postpone the issue to Chap. 5 In parallel, late-time non-linear large-scale structures and the possible detection of tiny primordial non-linear effects require to go beyond the first perturbative order. In preparation of this, we review some results on linear and non-linear perturbation theory.
Yet it is possible to see peril in the finding of ultimate perfection. It is clear that the ultimate pattern contains its own fixity. In such perfection, all things move toward death.
— Frank Herbert, Dune
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Notes
- 1.
This actually constitutes a major problem in the hot big bang model, which we shall meet soon. The problem will be solved eventually, hence the flatness assumption is justified.
- 2.
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Calcagni, G. (2017). Cosmological Perturbations. In: Classical and Quantum Cosmology. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-41127-9_3
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