Soon after he proposed three classic observational tests for the general theory of relativity, Einstein realised that a consistent description of the universe as a whole provided another important challenge for the theory. In this essay, we recall how general relativity found important application in the nascent field of cosmology, from the static models of Einstein and de Sitter to the expanding cosmologies of Friedmann and Lemaitre. By the early 1930s, the first tentative astronomical evidence of cosmic expansion had trigged a paradigm shift to dynamic cosmologies, almost all of which were couched firmly within the framework of general relativity. However, further progress was impeded for some years by a paucity of observational data. In the 1950s, the debate between steady-state and big bang models of the universe provided a new stimulus for the quest to determine key parameters of relativistic models of the cosmos by astronomical observation, setting the stage for today's precision cosmology.

In reply to Mike Follows’ review of Michael Strevens’ book The Knowledge Machine: How an Unreasonable Idea Created Modern Science.

Einstein's blackboard is a well-known exhibit at the History of Science Museum at Oxford University. However, it is much less well known that the writing on the board provides a neat summary of a work of historic importance, Einstein's 1931 model of the expanding universe. As a visual representation of one of the earliest models of the universe to be proposed in the wake of Hubble's observations of the nebulae, the blackboard provides an intriguing snapshot of a key moment in modern astronomy and cosmology. In addition, one line on the blackboard that is not in Einstein's 1931 paper casts useful light on some anomalies in the calculations of that paper.

We present a translation and analysis of a cosmic model published by Einstein in 1931. The paper, which is not widely known, features a model of a universe that undergoes an expansion followed by a contraction, quite different to his static model of 1917 or the monotonic Einstein-de Sitter model of 1932. The paper offers many insights into the cosmology of Albert Einstein in the light of the first evidence for an expanding universe, and we discuss his views of issues such as the curvature of space, the cosmological constant, the singularity and the timespan of the expansion. We argue that retrospective descriptions of this model as cyclic or periodic are not historically or mathematically accurate. We find that calculations in the paper of the matter density and radius of the universe contain a numerical error, a finding that is supported by writing on a blackboard used by Einstein during a lecture at Oxford University in May 1931. Our article concludes with a general discussion of his philosophy of cosmology.

A welcome new tome offers an incomplete portrait of a flawed genius

Description A welcome new tome offers an incomplete portrait of a flawed genius A welcome new tome offers an incomplete portrait of a flawed genius

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.

This article presents a brief review of some historical and philosophical aspects of Einstein's 1917 paper 'Cosmological Considerations in the General Theory of Relativity', a landmark work that denoted the starting point of modern theoretical cosmology. Our presentation includes a discussion of Einstein's early views of issues such as the relativity of inertia, the curvature of space and the cosmological constant. Particular attention is paid to lesser-known aspects of Einstein's paper such as his failure to test his model against observation, his failure to consider the stability of the model and a slight mathematical confusion concerning the introduction of the cosmological constant term. Taken in conjunction with his later cosmological works, we find that Einstein's approach to cosmology was characterized by a pragmatic search for the simplest model of the universe that was consistent with the principles of relativity and with contemporaneous astronomical observation.

We consider the proposal by many scholars and by the International Astronomical Union to rename Hubble’s law as the Hubble-Lemaître law. We find the renaming questionable on historic, scientific, and philosophical grounds. From a historical perspective, we argue that the renaming presents an anachronistic interpretation of a law originally understood as an empirical relation between two observables. From a scientific perspective, we argue that the renaming conflates the redshift/distance relation of the spiral nebulae with a universal law of cosmic expansion derived from the general theory of relativity. We note that the first of these phenomena is merely one manifestation of the second, an important distinction that might be relevant to contemporary puzzles concerning the current rate of cosmic expansion. From a philosophical perspective, we note that many of the named laws of science are empirical relations between observables, limited in range, rather than laws of universal application derived from theory.

Arthur Stanley Eddington was one of the leading astronomers and theorists of his generation and a prominent proponent of the general theory of relativity. Yet when his former assistant Georges Lemaitre sent him a paper in 1927 suggesting that the well-known redshifts of the spiral nebulae might be a manifestation of a cosmic expansion predicted by relativity, Eddington paid no attention for three years. In this paper, we consider the reasons for this oversight. We find that conventional explanations (such as Lemaitre's status as a relatively junior researcher and his decision to publish in a lesser-known Belgian journal) do not convince. We propose an alternative explanation that has not been considered in the literature - namely that the observational data cited by Lemaitre in support of his model were of a preliminary nature and would not have been sufficiently convincing for Eddington and others to consider non-static cosmologies.

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. 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 as a serious error and that he very likely 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.

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 Λ-CDM cosmology. We find that the cosmological constant was never truly banished from theoretical models of the universe, but was marginalized 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 Ia 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.

In response to the feature "The dark-energy deniers" (June pp21–24) by Keith Cooper, who speaks to those scientists who are still disagreeing over whether dark energy is the explanation for the expanding universe.

It is well known that in the early 1930s, Einstein banished the cosmological constant term from his cosmology. He is reputed to have later described the term as his biggest blunder, a statement that became one the great legends of 20th century physics. However, many doubts about the statement have been raised in recent years, not least because almost all references to it can be traced back to a single source, the maverick physicist George Gamow. In this paper, we interrogate the legend of Einsteinu0027s biggest blunder statement in the context of our recent studies of Einsteinu0027s cosmology in his later years. We find that the remark is very compatible with Einsteinu0027s cosmic models of the 1930s, with his later writings on cosmology, and with independent reports by two other physicists. We also find it quite plausible that Einstein made such a statement to Gamow in particular. We conclude that there is little doubt that Einstein came to view the introduction of the cosmological constant a serious error, and that it is very plausible that he labelled the term his biggest blunder on at least one occasion.

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.

The recent discovery that Einstein once attempted - and quickly abandoned - a steady-state model of the expanding universe sheds new light on his philosophical journey from static to dynamic cosmologies.

In reply to Robert P Crease's Critical Point article "This time it's different" (January pp19–20) in which he says that the election of Donald Trump as president of the US suggests that scientific authority is defunct.

In reply to the infographic "Nobel physics laureate migration" (November 2015 pp16–17, http://ow.ly/STSV7) and the accompanying article.