# Does the cosmological constant 'require' energy?

1. Nov 13, 2013

### Herbascious J

I have a question about GR in a cosmological setting. If dark energy is assumed to be a true GR cosmological constant, does this require some kind of energy input. I am curious to know if this is just a 'curvature' of space somehow, or does it represent a continual addition of energy on some level? I'm curious to know if energy is being created somehow. Also, is this energy negative or positive? Thanks!

2. Nov 13, 2013

### pervect

Staff Emeritus
The cosmological constant, in its usual form, has exactly the same gravitational effects as a positive energy density and a negative pressure.

Note that GR is different from the Newtonian mechanics to which you are probably used to. The source of gravity is not "mass", which becomes difficult to define in GR, but the stress energy tensor. The important components of the stress-energy tensor in cosomology are the energy density, rho, and the pressure P. These both have gravitational effects, and the effects of a cosomological constant are equivalent to a positive rho and a negative P. For the exact mathematical details of these effects, look up the Friedmann equations.

It is often assumed that the cosmological constant does has something to do with an actual positive energy density in the vacuum due to quantum effects, though efforts to calculate this don't give even close to the right order of magnitude and the "explanation" is open to considerable question.

There are some alternate forms of the cosmological constant known as quientessecne. The particular form I'm describing is the lambda-CDM concordance model.

3. Nov 13, 2013

### bcrowell

Staff Emeritus
In other words, are you asking about how conservation of energy plays out, with inputs and outputs of energy being balanced? GR has local but not global conservation of energy-momentum. Locally, the divergence of the stress-energy tensor is zero, and this is required if GR is to be self-consistent. This divergence-free property is interpreted as local conservation of energy-momentum. It is not violated by the existence of dark energy. For example, if dark energy behaves like a cosmological constant, then its divergence vanishes identically because the derivative of a constant is zero.

4. Nov 13, 2013

### TumblingDice

Leonard Susskind has a 2013 lecture series on Cosmology. It's a part of Stanford's Continuing Education program, so it has just enough math to understand the processes, equations, and foundations. Lecture #1 covers the Friedman equations and everything from inflation through expansion.

At this level I believe Lenny said that CC, DE, and VE are all different names for the same thing (cosmological constant, dark energy, negative vacuum energy). He explains energy density, rho, and p that pervect mentioned. If I recall correctly, energy density is a calculated value based on the estimate of all of the energy in the observable universe (a "constant" that includes mass and anything else that counts as energy) in relationship to the current "size" of the OU. So energy density isn't to be confused with dark energy or expansion. It's a part of calculating the geometry of the universe together with other values to postulate what should be expected under different scenarios.

I highly recommend watching at least lecture #1:

Last edited: Nov 13, 2013
5. Nov 13, 2013

### Herbascious J

Yes, that is basically what I was driving at... It seemed odd to me that things can accelerate with out an energy input. I understand that were talking about curvature of space and not mechanical motion, so I assumed it works out ( I guess gravity itself doesn't require energy input to cause acceleration, correct? so it's not surprising) However, if the universe is simply expanding, like in the Friedman models, things makes sense because there is constant velocity between objects, similar to newtons predictions. But, an over arching expansion that drives it's self more quickly as time passes seems like there needs to be energy to drive it. Thinking of a Newtonian explanation there would have to be a force, and therefore energy. But I think I understand, it's just a curvature of space, right? I think I would do well, to learn the math :)

Thanks for all the great replys!!!

6. Nov 13, 2013

### bcrowell

Staff Emeritus
Right. But locally, nothing accelerates. That's a matter of definition: in GR, we define an inertial frame to be the motion of a test particle. Globally, galaxies are accelerating relative to distant galaxies, but there is no global conservation of energy.

7. Nov 13, 2013

### PAllen

Here is my personal take on the difference between these:

1) Dark Energy is a poorly chosen name for a collection cosmological observations.

2) Vacuum energy is one attempt to explain these observations that, applied in a straightforward way, has failed miserably by predicting an effect many, many orders of magnitude larger than the observations.

3) The cosmological constant is simply an constant of integration in the equations of GR - a boundary condition, as it were. Taken as a purely classical theory, GR has no explanation of its boundary conditions, nor is it reasonable to expect one within GR. However, there is a precise prediction associated with the CC - since it is a constant in the equations, a specific behavior for expansion is mandated. Any confirmed deviation would preclude the CC as model (not explanation) of DE. As data has increased over decades, agreement with CC as a model has steadily increased, while ruling out a number of models that disagreed with CC.

At the moment, then, agreement with the CC model is taken as a requirement for any proposed explanation of DE.

8. Nov 15, 2013

### Naty1

yes...energy density is believed constant during the inflationary expansion believed to have followed the big bang.

yes it is; yet that appears to have happened very near the start of our universe and continues today over vast cosmological distances.

One possible explanation from another discussion in these forums:

Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 7 Sep 2012)
http://arxiv.org/abs/1209.1609

edit: [So your comment "I am curious to know if this is just a 'curvature' of space somehow.." IS insightful!]

but
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 6 Nov 2012)
http://arxiv.org/abs/1211.1354