Abstract
In early history of relativistic cosmology Alexander Friedmann (1923), in his book The world as space and time, modestly and wisely viewed cosmological models as “schematic and simplified, reminding one of the real world only to the extent that a dim reflection from a mirror of a schematic drawing of the cathedral of Cologne may be reminiscient of the cathedral itself”. Since those pristine days, cosmology has grown into an ambitious project dealing with applications of modern physics to the description of the largest observable universe. Here we first take a brief look at Newtonian cosmology and the first world model by Einstein and then describe the Friedmann model, the main theoretical tool in the hands of today’s cosmologists, which has developed into a many-component model containing ordinary matter, radiation, and, for the most part, dark unknown substances.
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Notes
- 1.
In this same study Arrhenius explains the absence of spiral nebulae close to the band of the Milky Way as due to the extinction of light by absorbing material. At that time and before, the odd distribution of nebulae was often regarded as evidence for their status as constituents of our Milky Way instead of being remote “Island Universes”.
- 2.
The parameters of the partial equations of state (7.17) and the associated “effective” one-fluid parameter (7.16) are related by γ=(wα+β)/(α+1). For a coherent model with constant equation of state parameters for matter (β) and dark energy (w), the associated one-fluid model also has γ= constant in p=γε.
- 3.
Because of the indirect, non-local measurement of distance, cosmological (metric) distances will always be tied to a cosmological model and tend have some unphysical aura around them (Samuel 2005).
- 4.
One may find it difficult to remember the difference between the two kinds of horizon. Note that here a particle refers especially to a photon which we observe (and which left its origin sometimes in the past 0→t 0), while “events” refer to phenomena all over the universe (and which will be observed or not sometimes in the future t 0→∞).
- 5.
Wolfgang Mattig has worked predominantly in the field of solar physics, and, as he mentioned in a letter to us, he never worked in extragalactic research and cosmology was his hobby. He derived the famous Mattig’s equation when he had to deliver a lecture on cosmology in connection with his doctoral thesis.
- 6.
We discuss here Friedmann models, but note that any developed non-Friedmann world model must also have its own redshift-distance (z–r) and redshift-time (z–t) relations and also the rules which relate luminosity and angular size distances to the metric distance r, in order to be able to predict observable effects and test these predictions (Chap. 8).
- 7.
A useful expression for the angular size distance for different dust-vacuum models was given by Demianski et al. (2003), accurate to 1.5% in the z range from 0 to 10.
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Baryshev, Y., Teerikorpi, P. (2012). The Friedmann Model. In: Fundamental Questions of Practical Cosmology. Astrophysics and Space Science Library, vol 383. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2379-5_7
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