Abstract
If we average over sufficiently large scales—on the order of 100 Mpc—our universe is homogeneous and isotropic to a high degree. We can therefore study what the Einstein equations tell us about the scale factor a(t) of the FLRW metric. But before we do this, we want to find out what we can infer about the time dependence of a(t) from ordinary Newtonian dynamics.
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- 1.
Friedmann, Alexander Alexandrovich, Russian physicist, *Saint Petersburg 16.6.1888, †Leningrad 16.9.1925.
- 2.
Robertson, Howard Percy, American mathematician and physicist, *27.1.1903 Hoquiam, †26.8.1961 Pasadena; Walker, Arthur Geoffrey, British mathematician, *17.7.1909 Waltford, †31.3.2001 West Chiltington.
- 3.
Note that
$$\begin{aligned} \mathcal {T}^{\mu \nu } = (\rho +P) u^\mu u^\nu - Pg^{\mu \nu }\;, \end{aligned}$$(8.29)where \(u^\mu \) is the four-velocity (cf. [12]).
- 4.
Adiabaticity of the expansion of the universe has in fact been an implicit assumption that we have made very early on. Without it we would not be able to absorb the full time dependence of the metric into the scale factor!
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Hentschke, R., Hölbling, C. (2020). Friedmann–Robertson–Walker Cosmology. In: A Short Course in General Relativity and Cosmology. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-46384-7_8
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DOI: https://doi.org/10.1007/978-3-030-46384-7_8
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