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Historical and philosophical reflections on the Einstein-de Sitter model

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Abstract

We present some historical and philosophical reflections on the paper “On the Relation Between the Expansion and the Mean Density of the Universe”, published by Albert Einstein and Willem de Sitter in 1932. In this famous work, Einstein and de Sitter considered a relativistic model of the expanding universe with both the cosmological constant and the curvature of space set to zero. Although the Einstein-deSitter model went on to serve as a standard model in ‘big bang’ cosmology for many years, we note that the authors do not explicitly consider the evolution of the cosmos in the paper. Indeed, the mathematics of the article are quite puzzling to modern eyes. We consider claims that the paper was neither original nor important; we find that, by providing the first specific analysis of the case of a dynamic cosmology without a cosmological constant or spatial curvature, the authors delivered a unique, simple model with a straightforward relation between cosmic expansion and the mean density of matter that set an important benchmark for both theorists and observers. We consider some philosophical aspects of the model and provide a brief review of its use as a standard ‘big bang’ model over much of the \(20{\mathrm {th}}\) century.

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Notes

  1. Despite hundreds of references to the paper, we are aware of only one article that notes that the Einstein–de Sitter paper is not a ‘big bang’ model (Kragh 1997).

  2. See (Kerzberg 1989; Realdi and Peruzzi 2009) for a discussion of this debate.

  3. This point is sometimes disputed and will be discussed further in Sect. 4.

  4. Equation (2) is a special case of the so-called Friedman equation, although the authors don’t state this. The Einstein constant \(\upkappa \) is given by \(\kappa =8\pi G/c^{2}\).

  5. As this equation is not numbered in the original paper, we use the label (2’) for reasons of clarity.

  6. We use the word ‘radius’ in a loose sense here, following de Sitter.

  7. The underlying reason for this is that the equation relating the Doppler shifts of the nebulae to cosmic expansion is given by \(R'/R =\textit{ v/cr}\) where r is the distance of the source (Lemaître 1927).

  8. We have given an analysis and first English translation of the paper in (O’Raifeartaigh and McCann 2014).

  9. This was a common assumption at the time (de Sitter 1930).

  10. A well-known anecdote from Eddington suggests that the authors themselves did not consider the work to be of great importance (Eddington 1940, p128; Nussbaumer and Bieri 2009, p152).

  11. Friedman’s paper of 1924 was not well-known.

  12. A similar observation can be made about the cosmologies of Hermann Weyl, Cornelius Lanczos and Howard P. Roberston (Nussbaumer and Bieri 2009, pp. 78–82).

  13. This could be labelled the ‘shut up and observe’ phase of cosmology in analogy with the well-known ‘shut up and calculate’ phase of quantum field theory (Kaiser 2011, pp. 1–25).

  14. Note for example that steady-state models predicted a value of \(q_{\mathrm {0}} = -1\).

  15. Strong observational evidence for the existence of dark matter emerged in the 1960s (Trimble 1990, 2013).

  16. It should be noted that many theorists never truly dropped the cosmological constant (O’Raifeartaigh et al. 2018).

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Acknowledgements

Cormac O’Raifeartaigh thanks Professor Jim Peebles, Professor G. F. R. Ellis and Dr. Phillip Helbig for helpful discussions. Simon Mitton thanks St Edmund’s College, University of Cambridge for the support of his research in the history of science.

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Authors and Affiliations

  1. School of Science and Computing, Waterford Institute of Technology, Cork Road, Waterford, Ireland

    Cormac O’Raifeartaigh & Michael O’Keeffe

  2. St Edmund’s College, University of Cambridge, Cambridge, CB3 0BN, United Kingdom

    Simon Mitton

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  1. Cormac O’Raifeartaigh
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Correspondence to Cormac O’Raifeartaigh.

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O’Raifeartaigh, C., O’Keeffe, M. & Mitton, S. Historical and philosophical reflections on the Einstein-de Sitter model. EPJ H 46, 4 (2021). https://doi.org/10.1140/epjh/s13129-021-00007-8

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