in 1917, Albert Einstein amazed the world of physics by publishing his general theory of relativity in which he describes gravity as a geometric property of space and time. That immediately raised the broader question of the structure of the universe as a whole, a problem that founded the modern discipline of cosmology.

In the next few years, various scientists developed various different models of the way the fabric of space time might be arranged in the cosmos, researchers such as the Russian physicist Alexander Friedmann, the Dutch mathematician Willem de Sitter and the Belgian priest Georges Lemaitre. Einstein played a relatively small part in these discussions, producing only a few important contributions.

At that time, the conventional thinking was that the universe existed in a steady-state, that it was neither expanding nor contracting. And for that reason, Einstein introduced a cosmological constant into his model that could be fine-tuned to ensure that the universe did not expand or contract.

But a key part of the jigsaw was missing. At about that time, Edwin Hubble began to publish data suggesting that the “island universes”, or galaxies, that astronomers could see were vastly more distant than the stars and moving away from us at rapid speed. His conclusion, one that profoundly changed our understanding of the cosmos, was that the universe must be expanding.

The leading physicists of the time immediately grasped the significance of Hubble’s discovery. If he was correct, the steady-state models of the universe would need to be changed.

Indeed, in 1932 Einstein and de Sitter published a new model in which they abandoned the cosmological constant and so allowed the universe to expand. This model has been the workhorse of the cosmological community ever since.

Now Cormac O’Raifeartaigh and Brendan McCann at the Waterford Institute of Technology in Ireland reveal an important step in the evolution of Einstein’s thinking towards this model. These guys have translated a little-known paper of Einstein’s for the first time that predates the 1932 paper by a year.

In this paper, called “Zum kosmologischen Problem der allgemeinen Relativitätstheorie” or “On the cosmological problem of the general theory of relativity”, Einstein creates a model universe that first expands and then contracts with a singularity at the beginning and at the end. This model is important because he also sets the cosmological constant to 0, thereby testing this idea for the first time.

O’Raifeartaigh and McCann begin by explaining the historical concept of the paper. Einstein appears to have written this paper after a three-month visit to the US where he spent much of his time at Princeton but also travel to meet Hubble and discuss his results.

One of the curious features of the paper is that Einstein misspells Hubble’s name throughout, suggesting to O’Raifeartaigh and McCann that he must have been unfamiliar with Hubble’s work. Neither is the paper carefully referenced, perhaps because Einstein clearly hurried to finish it. O’Raifeartaigh and McCann say he wrote it over a period of just four days.

The model that Einstein toys with is clearly a stepping stone. For example, it assumes a universe in which the fabric of space-time has a positive curvature. That was necessary in Einstein’s steady-state model of the universe. But he later discovered that it was unnecessary in an expanding model which could have positive or negative curvature or be flat. Indeed, the possibility that universe could be flat was one of the features of the Einstein-de Sitter model a year later.

One of the most interesting aspects of the paper is that Einstein uses this model to calculate the size of the universe, which he puts at 10^8 light-years or 9.5×10^25 centimetres in radius (several orders of magnitude smaller than today’s estimates).

To make this calculation, he estimates the age of the universe at about 10 billion years old. (The current consensus is that the universe is about 14 billion years old).

However, O’Raifeartaigh and McCann point out that it is by no means clear where Einstein gets his estimate; they assume from some earlier calculations by Friedmann. And they go on to point out that Einstein seems to have made a number of numerical errors in these calculations, again perhaps due to the short time he spent on the paper.

“Einstein seems something of an impatient cosmologist, rather than a scientist attempting to show that his greatest theory [is]compatible with some astonishing new astronomical observations,” they say.

That is an interesting insight into the evolution of Einstein’s thinking about the nature of the universe as well as into the man himself. Who has not hurried a piece of work and later found that it contains errors?

Incidentally, after the 1932 paper with de Sitter, Einstein showed little interest in cosmology, preferring to spend his time on the ultimately unsuccessful task of unifying relativity with quantum theory.

Einstein must be one of the most written about and well-studied scientists of all time. So it seems strange that his work is still being translated into English for the first time. But that’s why O’Raifeartaigh and McCann’s translation is a worthy addition to the body of work on this amazing man.

Ref: arxiv.org/abs/1312.2192 : Einstein’s Cosmic Model Of 1931 Revisited: An Analysis And Translation Of A Forgotten Model Of The Universe