Abstract
GR plays a central role in the grand domain of cosmology. Space does not allow us to give an adequate introduction to the vast field of modern cosmology. This last chapter of Part II contains only a concise treatment of the Friedmann–Lemaître models, together with some crucial observations that can be described within this idealized class of cosmological models. In particular, we derive the theoretical tools for the analyzes of the luminosity-redshift relation for type Ia supernovae, including the role of dynamical models of dark energy. The thermal history below about 100 MeV is discussed in detail, up to the point when electrons combine with protons and helium ions to form neutral atoms and the radiation decouples. In the introduction to this chapter, we sketch the early history of cosmology, which is not even well-known among cosmologists, and is often distorted. In particular, the key role of Lemaître in the founding period is not sufficiently appreciated. He was the first person who seriously proposed an expanding universe as a model of the real universe. He derived in his crucial paper of 1927 the general redshift formula, and showed that it leads for small distances to a linear relation—known as Hubble’s law—two years before Hubble’s famous work.
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- 1.
By Universe I always mean that part of the world around us which is in principle accessible to observations. In my opinion the ‘Universe as a whole’ is not a scientific concept. When talking about model universes, we develop on paper or with the help of computers, I tend to use lower case letters. In this domain we are, of course, free to make extrapolations and venture into speculations, but one should always be aware that there is the danger to be drifted into a kind of ‘cosmo-mythology’.
- 2.
Consult the Home Page: http://www.mso.anu.edu.au/2dFGRS.
- 3.
See the Home Page: http://www.sdss.org/sdss.html.
- 4.
- 5.
Even if B, L e , L μ , L τ should not be strictly conserved, this is not relevant within a Hubble time \(H_{0}^{-1}\).
- 6.
Beside the (bolometric) magnitudes m,M, astronomers also use magnitudes m B ,m V ,… referring to certain wavelength bands B (blue), V (visual), and so on.
- 7.
This is perhaps not so astonishing, because the progenitors are presumably faint compact dwarf stars.
- 8.
Recently it has convincingly been demonstrated that the supernova remnant SNR 0509-67.5 (the site of a type Ia supernova 400±50 years ago) in the Large Magellanic Cloud originated from such an event. See [311].
- 9.
For this case the following calculations become a bit simpler if one makes use of the general fact that null geodesics remain null geodesics under conformal changes of the metric.
- 10.
Recall that the Lie derivative (directional derivative) L X of a function f on a manifold with respect to a vector field X can be obtained from the total derivative along an integral curve x(λ) of X from the relation
$$\frac{d}{d\lambda}f\bigl(x(\lambda)\bigr)= (L_Xf) \bigl(x(\lambda) \bigr). $$ - 11.
Since this book contains only a modest introduction to cosmology, we give references to some useful recent textbooks.
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Straumann, N. (2013). Essentials of Friedmann–Lemaître Models. In: General Relativity. Graduate Texts in Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5410-2_10
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