In science literature and online sources, the whole universe is often depicted in the shape of a cylinder.
In year 2018, I completed my first book (on the topic of big bang) but a perplexing issue remained outstanding which I could not solve till the publication of the book. The problem was that Friedmann (1922) was saying that Einstein’s depiction of universe was cylindrical whereas Einstein’s own paper (1917) had described universe as spherical.
Following is quote from Friedmann (1922) paper:
In their well-known works on general cosmological questions, Einstein and de-Sitter arrive at two possible types of universe: Einstein obtains the so-called cylindrical world ……..
Whereas if we read Einstein (1917) paper, we find that Einstein was talking about spherical universe:
From our assumption as to the uniformity of distribution of the masses generating the field, it follows that the curvature of the required space must be constant. With this distribution of mass, therefore, the required finite continuum of the x1, x2, x3 with constant x4, will be a spherical space.
Here x1, x2 and x3 are coordinates of three dimensional space and 4th dimension x4 (time) is kept constant and the result is a spherical space.
So the issue remain unresolved till the publication of my book (2018) regarding why did Friedmann (1922) write that Einstein (1917) had obtained a cylindrical universe. However, now I get the clue of this apparent anomaly. It turned out that Friedmann (1922) had taken his understanding of Einstein (1917) from Arthur Eddington’s (1921) book i.e. a secondary source. Following is written in Eddington (1921) book:
It is with some such underlying idea that Einstein’s cylindrical space-time was suggested, since this cannot exist without matter to keep it stretched. Now we freely admit that our assumption of perfect flatness in the remote parts of space was arbitrary …..Space, Time and Gravitation, An outline of the General Relativity (1921)
Now case is clear before the readers. Einstein (1917) was talking about three dimensional space as spherical while keeping 4th dimension (time) as constant. Eddington (1921) was talking about 4 dimensional space-time to be cylindrical in shape. Friedmann (1922) was talking about three dimensional space and calling it cylindrical on behalf of Einstein.