# What are the differences between dark energy and a cosmological constant?

My possibly mistaken understanding is that dark energy changes with time, whereas a cosmological constant is, well, constant. What about gravitational clumping? Detecting relative motion?

## 4 Answers

Dark energy is a catch all term for whatever is accelerating the expansion. The simplest form of dark energy consistent with general relativity is a cosmological constant, and this is just an energy density per unit volume of space.

The cosmological constant is time independant (and position independant) by definition, that is if it were changing in time or space it wouldn't be called a cosmological constant. You can replace the cosmological constant with a scalar field that is allowed to vary in space and/or time, and this gives rise to other models such as quintessence. It's interesting to speculate about ideas like this, but at the moment there is no evidence that the dark energy is changing, and therefore a simple cosmological constant is consistent with observations.

You need to bear in mind that the cosmological constant and quintessence are just mathematical models that fit the observed data. At the moment there is no theoretical reason to recomend the cosmological constant, quintessence or indeed anything else.

The Wikipedia article you linked discusses the various forms of dark energy. Can you expand a bit on what issues the article leaves you unsure about.

• Actually, I didn't supply those wikipedia links, Qmechanic did, thank you very much. I have read the links and they support both the time constancy and the gravitational clumping as possible differences, (but below today's level of sensitivity.) I found nothing about relative motion however. We have detected our motion relative to the CMB. If we were not at rest relative to the quintessence field, could we detect that, (assuming we could detect the quintessence field)? – Jim Graber Sep 2 '12 at 17:41
• Good question. Motion makes no difference to the cosmological constant, but I don't know if it would affect quintessence. I imagine it would depend on the form it takes. – John Rennie Sep 2 '12 at 18:24

Short and sweet: A cosmological constant is the special case of dark energy with constant density; Dark Energy may also be non-constant, we do not know if this is actually the case.

• Actually, the first law of thermodynamics proves that dark energy cannot remain at constant density despite the expansion of the universe, if it behaves like all other forms of energy that we know about. All other forms of energy have gravity, as they warp space/time by their existence, all forms of propulsion have limits. The gravity of dark energy itself will collapse the universe once the propulsion or outward pressure it exerts like hot air in a balloon stops or slows enough for the limitless force of gravity to take over. There is no reason to think it's any different to any other energy. – rowanman28 Mar 3 '15 at 5:05
• So (why) does anybody still scratch their heads over dark energy instead of simply concluding that the cosmological constant is non-zero? – Adrian May Jul 21 '15 at 9:08
• @rowanman28 Acytually, the (Almost)-constant-density condition is pretty much the very definition of DE. So no, your comment is not correct. – Thriveth Jul 21 '15 at 21:54
• @AdrianMay Because that would be a non-answer, since the Cosmological Constant is just a different name for (a special case of) Dark Energy. – Thriveth Jul 21 '15 at 21:56
• But if Einstein had no reason to set it to zero in the first place, and if there's no empirical evidence for any more complex version of dark energy, then it's a non-question ;-) – Adrian May Jul 24 '15 at 2:48

As noted dark energy is a catch all term to explain accelerated expansion.

In most general terms dark energy must be of a form such:

($\rho_{dark \: energy} + \rho_{all \: other \: matter}) + 3(P_{dark \: energy} + P_{all \: other \: matter}) <0$

Where $\rho$ is energy density and $P$ is pressure (they have the same units).

As all other terms are non-negative, $P_{dark \: energy}$ must be negative, i.e. dark energy has negative pressure and further $\frac{P_{dark \: energy}}{\rho_{dark \: energy}} < -\frac{1}{3}$ (this is the bear minimum to make sure that dark energy doesn't have the effect of slowing the expansion of the Universe)

The cosmological constant is dark energy of the form $\frac{P_{dark \: energy}}{\rho_{dark \: energy}} = -1$ and its energy density remains constant as the Universe expands, though the dark energy of the form where the energy density increases and of the form where the energy density decreases are both allowed by the above.

My view is that dark energy is like hot air in a balloon. It's density does not stay constant, but decreases as the universe expands, like every other form of energy.

Like other forms of energy, it would also be subject to the second law of thermodynamics and would cool down, slow down, and get sucked into black holes, converting it's pushing effect, into a pulling effect of gravity.

There's no reason to think it behaves completely differently to all other forms of energy we know about.

• There is reason to believe it behaves differently. See for instance my answer to your question physics.stackexchange.com/q/105533 for some ideas to get you thinking. – Kyle Oman Mar 28 '14 at 21:06
• Maybe it's quintessence that I'm talking about, I don't really know, but nobody has explained how dark energy is not the same energy that makes us up, made of a certain number of sub-atomic particles or strings, which could not increase in number, unless defying the first law of thermodynamics. Observations do not suggest that this basic law needs to be broken, it's to do with calculations which make more sense if it is a constant density, even though I can't see how that's possible. Einstein suggested the constant to explain a static non expanding universe. – rowanman28 Apr 3 '14 at 6:13
• In quintessence/phantom-dark-energy the dark energy per volume may as well increase while the volume itself also increases. – Yukterez Mar 1 '15 at 22:28
• No, that's impossible. Dark energy like all things is made of measurable amounts of particles or individual bits of energy, no matter how small they may be, and the amount of strings or whatever it is they are in dark energy cannot increase, because that would be energy just making itself out of nothing, breaking the first law of thermodynamics. – rowanman28 Mar 3 '15 at 4:45