# Cosmological constant doubts

I have read about cosmological constant given by einstein in universe in nutshell as well as in general and special relativity. But still I am not able to understand the aim to use it or to introduce it. Can someone explain in brief.

• define brief. Also, can you include your current level of understanding of the concept so any answerer might know where to start? – Jim Apr 16 '14 at 18:28
• Misner, Thorne and Wheeler's tome on GR explain clearly the effects of introducing a cosmological constant. – JamalS Apr 16 '14 at 18:35
• @JamalS haha 'tome', that sounds almost mythical to me :) – Danu Apr 16 '14 at 20:03
• @Danu: A hard copy of MTW is absolutely huge, almost mythical :) I don't know anyone that's ever gone through every page; it's still a great text. The only other text I know that comes close in size is Witten's text on superstring theory. – JamalS Apr 16 '14 at 20:07
• @Danu: I also have a digital copy... legally obtained of course... The file's so large whenever I try using the search tool my laptop freezes :) – JamalS Apr 16 '14 at 20:09

The cosmological constant has an interesting history behind it. Originally, when Einstein introduced his theory of general relativity in the early 20th century, the Einstein Field Equation, which was the equation for the gravitational field, described gravity as the effect of the curvature of space-time due to the presence of matter and energy. Perhaps you have seen the equation already, for it is:

$R_{\mu\nu}$-$1/2Rg_{\mu\nu}$=$kT_{\mu\nu}$

However, Einstein's equation predicted that the influence of gravity would cause the universe to either collapse on itself or expand. Such a prediction contradicted Einstein's view, for he believed that the universe was infinite and static, or never changing. Thus, he introduced the cosmological constant as a small energy density contribution required to stop the collapsing or expanding force of gravity and to keep the universe in balance. The new equation became:

$R_{\mu\nu}$-$1/2Rg_{\mu\nu}+\Lambda g_{\mu\nu}$=$kT_{\mu\nu}$

Where the lambda is the cosmological constant. However, Hubble's discovery that the universe was indeed not static but expanding (about a decade later after the cosmological constant was introduced) made Einstein's constant unnecessary. Due to this, Einstein supposedly called his introduction of the constant the "biggest blunder of my life." The constant was dropped for many decades until recently scientists discovered that the universe is accelerating in its expansion. The constant was then reintroduced is some inflation theories to describe the small energy density that propels such an accelerated expansion of the universe. The other answers to this question pretty much discuss its current uses. So after all, Einstein may have been right about the constant!

• +1 The OP is not a physicist (see profile) and he mentions a non technical book (Universe in a nutshell). So this is by far the clearest and probably most satisfying answer to his question. – magma Apr 17 '14 at 15:47
• It may also be worth mentioning that Einstein's "solution" to make the universe static would not be stable in any case, Hubble expansion or not, i.e. although equilibrium can be achieved, any small "bump" in the matter distribution would reinforce itself in positive feedback. So it's likely that $\Lambda$ would not have survived long as an "explanation" for a static universe even if Hubble's discovery had not been made. – WetSavannaAnimal Apr 18 '14 at 9:53

The cosmological constant is important for at least two reasons.

1. Our universe is currently asymptotically evolving towards a universe where a constant energy density dominates the total energy density. The cosmological constant can be interpreted as exactly this. Therefore, analysis of the current state of our universe relies heavily on the concept of a cosmological constant, even if we don't know how it arises.
2. inflationary theory, which has recently received strong experimental support from the BICEP2 experiment, asserts that the early universe went through a de Sitter-like epoch during which it underwent exponential expansion, driven by a large (quasi-)constant energy density (i.e. effective cosmological constant).

Thus, the cosmological constant is acutely relevant to both the past and future of our universe. This is an extremely condensed account and could be expanded immensely. It is also interesting for historical reason, and because 'why not?'.

• I would just add that our universe is currently "evolving towards a universe where a seemlingly constant energy density dominates the total energy density". It is not for certain that the Dark Energy has constant equation of state $w = -1$ This indeed fits the observations, and is one of two leading models to explain the late universe accelerating cosmic expansion, but there are dozens of other models in which the cosmoligical constant does not in fact have to be constant, but rather evolves throughout the history of the universe. There is no universally accepted model yet. – Flint72 Apr 16 '14 at 20:11
• @Flint72 I would say that the $\Lambda-CDM$ model is universally accepted, both from experience with researchers and googling, heh. 'Standard model of cosmology' yields en.wikipedia.org/wiki/Lambda-CDM_model as top hit, with no competitors in sight ;) – Danu Apr 16 '14 at 20:14
• sorry, yes indeed the $\Lambda \mbox{CDM}$ is known as the Stantard Model of Cosmology, but like the Standard Model of Elementary Particle Physics, we know that this is just a partial answer with lots left to be worked out. I was reffering specifically about the negative pressure dark fluid, which is, as you say, in $\Lambda \mbox{CDM}$ a cosmoligical constant with equation of state $w = -1$ However, most theories which try to give late universe accelerating cosmic expansion without simply adding it in by hand use an additional scalar field, such as Quintessence, say... – Flint72 Apr 16 '14 at 20:30
• ...this is only one of many, though the most common of them. I did not mean to sound like I was toting crazy theories, so I will remove it if you like. I just didn't want this questioner to think that it is fully accepted that the Dark Energy is a cosmological constant. To re-quote wikipedia, the Dark Energy article discusses both Cosmological Constant and Quintessence as possible explinations, as well as having a section on Alternative Ideas, of which there are many more besides those mentioned in that article. – Flint72 Apr 16 '14 at 20:39
• No, by all means leave your comment. Discussion is always good. I think my main point is that, even if dark energy isn't 'just a cosmological constant', the fact it can be modeled so incredibly well by one tells us that the cosmological constant is worth studying! – Danu Apr 16 '14 at 20:41

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