###### By Don Lincoln, Fermilab

## Albert Einstein was a brilliant man and a bit of a visionary. Certainly, his special and general theory of relativity revolutionized our understanding of the nature of gravity and the structure of the cosmos. He actually proposed and then retracted something akin to dark energy.

### Theory of General Relativity and Static Universe

Remember that Einstein invented general relativity in 1915 and it was first validated in 1919 by Sir Arthur Eddington. In the early days of general relativity, most astronomers believed that the universe was fixed, static, unchanging and eternal. In the Latin, it was said to be, *Sic semper erat, et sic semper erit*, or roughly translated, “Thus has it always been, and thus shall it ever be”.

This view of the cosmos was a sensible one for the year 1915 or so. After all, our telescopes could image stars of the Milky Way galaxy and some unidentified smudges on the photographic plates from telescopes that we now know to be galaxies. Our modern concept of the universe as galaxies peppering the universe was in the far future.

### Einstein’s Equations: A Failure?

Shortly after Einstein published his theory of relativity in 1915, it became evident that his equations did not predict a static universe. While Einstein did some preliminary work as early as 1917, it is Russian mathematician Aleksandr Friedmann who gets credit for properly understanding the implications of Einstein’s equations on the structure of the universe.

In 1922, Friedmann realized that Einstein’s equations predicted that a static universe would be unstable and that there were several different outcomes for the future of the universe. Gravity would cause it to collapse. Thus, it was suggested that Einstein’s equations were an abject failure.

Friedmann went on to predict all possible expected behaviors of any universe, which is to say: expand and contract, expand and never stop, and expand and eventually stop. He had long correspondences with Einstein who was a firm believer in the unchanging grandeur of the universe.

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### Einstein’s Addition to the Equation

Einstein thus decided to modify his equations to protect against the inevitable collapse of the universe due to gravity. He added a term to his equations that included a form of energy that repelled gravity’s tug.

If you’re an equation person, Einstein’s general relativity can be written in a super simple form. Basically, it’s a *G *with some subscripts equals a *T* with some subscripts, multiplied by a handful of constants. The *G* term tells space and time how to curve, while the *T* term tells matter and energy how to move. The curvature of space tells matter how to move.

What Einstein did was to add on the side of the *G* term another term, which is the capital Greek letter *lambda* times a little *g* with some subscripts. The little *g* simply tells how to measure the distance between two points, but the *lambda* was the big new addition.

*Lambda* is called the cosmological constant and it added a constant energy density to Einstein’s equations. This energy density was a repulsive form of gravity and, with it, Einstein made his equations robust against gravity’s attractive force. He had his unchanging and eternal universe back.

### Einstein’s ‘Biggest Blunder’

Of course, Hubble’s first inkling of the expanding universe occurred to him as early as 1924, and his big paper was released in 1929. The idea of a static universe was no longer a credible one. Einstein was at some level relieved, as he always found the addition of the *lambda* term to be, at best, inelegant.

He is said to have referred to the addition of the cosmological constant as his biggest blunder and removed it from all of his subsequent papers.

There have been some who have questioned whether Einstein ever actually ever said the specific phrase that the cosmological constant was his biggest blunder. For a long time, the only actual reports that he said that came from George Gamow, a younger and very successful physicist in his own right. Gamow was a prankster and fond of a tall tale now and again, which led some to question the veracity of the “biggest blunder” quote, but more recent scholarship has uncovered correspondence by other Einstein’s contemporaries that say roughly the same thing.

### Is Dark Energy and Einstein’s Cosmological Constant the Same?

Dark energy and the cosmological constant: are they the same thing? No. Actually, they may be, but in principle, no. The term “dark energy” is a phrase coined for whatever is the cause of the accelerating expansion of the universe. It’s simply a vague term for an unexplained phenomenon.

The term “cosmological constant” is a specific proposed model for dark energy. It’s a mathematical construct. Like the name suggests, it is cosmological in nature. It permeates the universe and it controls its future. It is also a constant density of energy.

### Common Questions about Einstein’s Cosmological Constant

**Q: How did astronomers view the universe in relation to the theory of general relativity?**

Einstein invented general relativity in 1915 and it was first validated in 1919 by Sir Arthur Eddington. In the early days of general relativity, most astronomers believed that the universe was fixed, static, unchanging and eternal. In the Latin, it was said to be, *Sic semper erat, et sic semper erit*, or roughly translated, “Thus has it always been, and thus shall it ever be”.

**Q: Who pointed out the failure of Einstein’s equations?**

In 1922, the Russian mathematician Aleksandr Friedmann realized that Einstein’s equations predicted that a static universe would be unstable and that there were several different outcomes for the future of the universe. Gravity would cause it to collapse. Thus, it was suggested that Einstein’s equations were an abject failure.

**Q: What did Einstein add to his equation?**

Einstein modified his equation and added on the side of the *G* term another term, which is the capital Greek letter *lambda* times a little *g* with some subscripts. The little *g* simply tells how to measure the distance between two points, but the *lambda* was the big new addition.*Lambda* is called the cosmological constant and it added a constant energy density to Einstein’s equations. This energy density was a repulsive form of gravity and, with it, Einstein made his equations robust against gravity’s attractive force.