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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 prototype 'big bang' model over much of the 20th century., Comment: Some revisions and corrections to original MS. Accepted for publication in the European Physical Journal (H)

Georges Lemaitre was a remarkable contributor to the advancement of cosmology in the heady years following two great revolutions in theoretical physics in the last century: general relativity and quantum mechanics. In the present century, the impact of his key publications has advanced from very little to enormous. The Big Bang universe has reigned supreme in cosmology for sixty years, during which time it has acquired paradigmatic status as the most important event in the entire history of cosmology. Lemaitre was the first cosmologist to estimate the rate of expansion of the universe, later known as the Hubble constant. In 2018 the International Astronomical Union renamed the Hubble law as the Hubble-Lemaitre law in acknowledgement of his foundational contribution to the theory of the expanding universe. This biographical review examines: (a) factors that influenced his approach to the philosophy of science, particularly cosmology; (b) his engagement with the network of contemporary cosmologists; and (c) the circumstances of his withdrawal from research in cosmology and the further promotion of the fireworks universe after the early 1930s., Comment: 19 pages, 8 images (photographs)

It is well known that, following the emergence of the first evidence for an expanding universe, Albert Einstein banished the cosmological constant term from his cosmology. Indeed, he is reputed to have labelled the term, originally introduced to the field equations of general relativity in 1917 in order to predict a static universe, his "biggest blunder". However serious doubts about this reported statement have been raised in recent years. In this paper, we interrogate the legend of Einstein's "biggest blunder" statement in the context of our recent studies of Einstein's cosmology in his later years. We find that the remark is highly compatible with Einstein's cosmic models of the 1930s, with his later writings on cosmology, and with independent reports by at least three physicists. We conclude that there is little doubt that Einstein came to view the introduction of the cosmological constant term a serious error and that it is very likely that he labelled the term his "biggest blunder" on at least one occasion. This finding may be of some relevance for those theoreticians today who seek to describe the recently-discovered acceleration in cosmic expansion without the use of a cosmological constant term., Comment: Revised version. Published in Physics in Perspective 20 (2018) 318-341

We present a centennial review of the history of the term known as the cosmological constant. First introduced to the general theory of relativity by Einstein in 1917 in order to describe a universe that was assumed to be static, the term fell from favour in the wake of the discovery of the expanding universe, only to make a dramatic return in recent times. We consider historical and philosophical aspects of the cosmological constant over four main epochs: (i) the use of the term in static cosmologies (both Newtonian and relativistic); (ii) the marginalization of the term following the discovery of cosmic expansion; (iii) the use of the term to address specific cosmic puzzles such as the timespan of expansion, the formation of galaxies and the redshifts of the quasars; (iv) the re-emergence of the term in today's Lamda-CDM cosmology. We find that the cosmological constant was never truly banished from theoretical models of the universe, but was sidelined by astronomers for reasons of convenience. We also find that the return of the term to the forefront of modern cosmology did not occur as an abrupt paradigm shift due to one particular set of observations, but as the result of a number of empirical advances such as the measurement of present cosmic expansion using the Hubble Space Telescope, the measurement of past expansion using type SN 1a supernovae as standard candles, and the measurement of perturbations in the cosmic microwave background by balloon and satellite. We give a brief overview of contemporary interpretations of the physics underlying the cosmic constant and conclude with a synopsis of the famous cosmological constant problem., Comment: 60 pages, 6 figures. Some corrections, additions and extra references. Accepted for publication the European Physical Journal (H)

We present a historical review of Einstein's 1917 paper 'Cosmological Considerations in the General Theory of Relativity' to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a natural next step after Einstein's development of the general theory of relativity and that the work offers many insights into his thoughts on relativity, astronomy and cosmology. Our review includes a description of the observational and theoretical background to the paper; a paragraph-by-paragraph guided tour of the work; a discussion of Einstein's views of issues such as the relativity of inertia, the curvature of space and the cosmological constant. Particular attention is paid to little-known aspects of the paper such as Einstein's failure to test his model against observation, his failure to consider the stability of the model and a mathematical oversight concerning his interpretation of the role of the cosmological constant. We recall the response of theorists and astronomers to Einstein's cosmology in the context of the alternate models of the universe proposed by Willem de Sitter, Alexander Friedman and Georges Lemaitre. Finally, we describe the relevance of the Einstein World in today's 'emergent' cosmologies., Comment: Revised version of paper with some edits and corrections. Accepted for publication in the European Physical Journal (H)

This paper celebrates the remarkable life, science and legacy of Abb\'e Georges Lema\^itre, the Belgian cleric and professor of physics; he was the architect of the fireworks model for the origin of the universe. He died half a century ago, three days after learning that Arno Penzias and Robert Wilson had discovered the cosmic microwave background. Despite being gravely ill from leukaemia, Lema\^itre lucidly praised this news, which confirmed the explosive genesis of our universe., Comment: Talk given on 11 November 2026 at the Ordinary Meeting of the Royal Astronomical Society

We recently reported the discovery of an unpublished manuscript by Albert Einstein in which he attempted a 'steady-state' model of the universe, i.e., a cosmic model in which the expanding universe remains essentially unchanged due to a continuous formation of matter from empty space. The manuscript was apparently written in early 1931, many years before the steady-state models of Fred Hoyle, Hermann Bondi and Thomas Gold. We compare Einstein's steady-state cosmology with that of Hoyle, Bondi and Gold and consider the reasons Einstein abandoned his model. The relevance of steady-state models for today's cosmology is briefly reviewed., Comment: To be published in the 'Proceedings of the 2014 Institute of Physics International Conference on the History of Physics', Cambridge University Press. arXiv admin note: substantial text overlap with arXiv:1504.02873, arXiv:1402.0132

We present a first English translation and analysis of a little-known review of relativistic cosmology written by Albert Einstein in late 1932. The article, which was published in 1933 in a book of Einstein papers translated into French, contains a substantial review of static and dynamic relativistic models of the cosmos, culminating in a discussion of the Einstein-de Sitter model. The article offers a valuable contemporaneous insight into Einstein's cosmology in the 1930s and confirms that his interest lay in the development of the simplest model of the cosmos that could account for observation, rather than an exploration of all possible cosmic models. The article also confirms that Einstein did not believe that simplistic relativistic models could give an accurate description of the early universe., Comment: Accepted for publication in the European Physical Journal (H). Includes an English translation of a little-known review of cosmology written by Albert Einstein in 1933. 20 pages, 4 figures

We present a translation and analysis of an unpublished manuscript by Albert Einstein in which he attempted to construct a 'steady-state' model of the universe. The manuscript, which appears to have been written in early 1931, demonstrates that Einstein once explored a cosmic model in which the mean density of matter in an expanding universe is maintained constant by the continuous formation of matter from empty space. This model is very different to previously known Einsteinian models of the cosmos (both static and dynamic) but anticipates the later steady-state cosmology of Hoyle, Bondi and Gold in some ways. We find that Einstein's steady-state model contains a fundamental flaw and suggest that it was abandoned for this reason. We also suggest that he declined to explore a more sophisticated version because he found such theories rather contrived. The manuscript is of historical interest because it reveals that Einstein debated between steady-state and evolving models of the cosmos decades before a similar debate took place in the cosmological community., Comment: 22 pages, 2 figures. Includes first English translation of unpublished Einstein manuscript. Accepted for publication in Eur.Phys.J.(H)