My extended series of write-ups on the Big Bang and inflationary cosmology is nearing a close. Tonight, I will write about Einstein's cosmological constant, and then later on, I'll have a piece on Alan Guth's ideas on inflation. I will sometimes use "CC" as an abbreviation for the cosmological constant, although in scientific circles it is referred to by the Greek letter lambda (Λ).
Einstein intended the cosmological constant for one purpose, then jettisoned it as a mistake after the original premise for its use was discredited. Other physicists and cosmologists later resurrected the CC, however, for use in a different context. As Dan Hooper's book Dark Cosmos explains:
Einstein... had originally introduced the cosmological constant into his equations in order to force the mathematics to provide a Universe that was static, neither expanding nor contracting. Although he later abandoned this extra term after Hubble's observations demonstrated that the Universe was in fact expanding, today it seems that perhaps he shouldn't have been so eager to throw away this extra piece of mathematics after all.
...The value of the cosmological constant originally chosen by Einstein led to a static and unchanging Universe. But with a different value, it is also possible for such a term to cause the expansion of the Universe to accelerate over time (p. 168).
Georges Lemaitre, the subject of John Farrell's book The Day Without Yesterday(which I reviewed here), was one scientist who tried to convince Einstein to put the CC to new use. In this way, the CC would fit with Lemaitre's ideas of a Big Bang and expanding universe. Writes Farrell:
In July 1947 Lemaitre wrote a letter to Einstein -- the last of their correspondence that survives -- in which he tried, once again, to persuade the founder of the general theory of relativity to reconsider his dismissal of the cosmological constant(p. 159).
[To Lemaitre and Sir Arthur Stanley Eddington, the] cosmological constant was not an arbitrary number, not a number picked out of thin air merely to balance the force of gravity. For them Λ represented something more, something physical. Lemaitre in particular began to treat the constant as the indicator of an actual force with a special role to play in an expanding universe(pp. 164-165).
Einstein's cosmological constant today is sometimes juxtaposed with the concepts of dark energy (a hypothetical entity driving the universe apart in an expansion) and vacuum (empty space) energy. Lemaitre's idea in the previous paragraph of an expansionary "force" also has some apparent similarity (to me at least) with Guth's model of inflationary cosmology, which I shall address in my next posting.
Back to our main discussion, the CC, dark energy, and vacuum energy all are proposed to account for the accelerated expansion of the universe observed in recent years.
A New York Times article from just a couple of weeks ago, after describing Einstein's abandonment of the CC, notes that "...quantum physics resurrected it by showing that empty space should be foaming with energy that had the properties of Einstein’s constant." However, a problem attends this formulation: "Alas, all attempts to calculate the amount of this energy come up with an unrealistically huge number, enough energy to blow away the contents of the cosmos like leaves in a storm before stars or galaxies could form. Nothing could live there."
Thus, to fit with observable nature, the CC must be much smaller than expected. Again quoting from the Times article, "But if dark energy is the cosmological constant, it is smaller than predicted by a shocking factor of 10^60 [10 raised to the 60th power]."
University of California Riverside professor John Baez has written a piece explaining the difficulties involved in determining the energy density of the vacuum. As he discusses, within the framework of Einstein's general relativity, a few steps are needed to understand the estimation of the energy density:
"...we've known for a long time that the universe is expanding... [and] this expansion is speeding up."
"...negative pressure makes the expansion tend to speed up."
Under the necessary conditions, the vacuum "must have a pressure equal to exactly -1 times its energy density..."
"From this, it follows that if the vacuum has positive energy density, the expansion of the universe will tend to speed up! This is what people see. And, vacuum energy is currently the most plausible explanation known for what's going on. ...the basic fact that the energy density of spacetime is very close to zero is almost unarguable: for it to be false, general relativity would have to be very wrong."
Other approaches, based in quantum field theories, yield other estimates.
Noting that "the conventionally defined cosmological constant Λ is proportional to the vacuum energy density PΛ," Sean Carroll concludes that, "If the recent observational suggestions of a nonzero Λ are confirmed, we will be faced with the additional task of inventing a theory which sets the vacuum energy to a very small value without setting it precisely to zero."
Another problem cited in the Times article: "Nor is there any solid evidence yet that dark energy is or is not varying with time — if it is not constant, it cannot be Einstein’s constant."
In light of the various conundrums involving the CC, vacuum energy, and dark energy, another theory being considered by some scientists is quintessence.
Finally, if your curiosity about Einstein's cosmological constant still has not been satiated, this University of Colorado page provides a seven-part, Q&A style, rundown of important themes.