# Is lambda a true force?

1. Feb 11, 2006

### Gerinski

Lambda (the cosmological constant) is frequently refered to as a sort of "negative gravity": instead of attractive it's repulsive, and instead of getting weaker with distance it gets stronger.

However in General Relativity gravity is not regarded as a true force, but just as the manisfestation of spacetime's geometry on the movement of matter and energy.

1. Is lambda a true force or just a geometrical distortion like gravity?
If a true force, is it expected to have a carrier particle associated?

2. Does lambda act on matter/energy, or on the fabric of spacetime itself? (would a region of spacetime devoid of any matter/energy stretch due to lambda? or only if it contains matter/energy?)

3. How the hell can we conceive of any influence that gets stronger with distance?
Is not distance, by definition, a concept that "separates"? that makes 2 points in spacetime less likely (or needing longer time) to influence eachother?
What could be a conceivable mechanism that allows lambda to have a stronger interaction with something distant than with something close?

4. Is lambda's influence supposed to propagate at the speed of light?

Last edited: Feb 11, 2006
2. Feb 11, 2006

Staff Emeritus
Umm, wouldn't lambda be just more geometry? Describing the shape of the spacetime manifold in time, i.e. its pattern of expansion?

3. Feb 11, 2006

### AlphaNumeric

The equation for the potential of the Strong interaction is $$V = \frac{\alpha}{r} + kr$$. The linear term increases the potential with distance.

4. Feb 11, 2006

### Gerinski

Yes, we know it does increase with distance, and the mathematical expression just reflects it.
But what mechanism or physical principle may account for such an exceptional behaviour?

5. Feb 11, 2006

### Hurkyl

Staff Emeritus
Why couldn't we conceive of such a thing?

Besides, we've known of such things for a long time. E.g. Hooke's law.

6. Feb 11, 2006

### Gerinski

Yes, you're right, but you surely understood my meaning. We can conceive it as in Hooke's law because we understand why (the distant points in question are materially connected, being part of a single (elastic) body)).
The real question was, do we have a physical mechanism explaining why lambda is stronger between distant bodies than between nearby ones?

7. Feb 11, 2006

### dicerandom

I don't know what you mean by it gets stronger with distance. Lambda is something that comes out of solutions of Einstein's field equations, it's an arbitrary constant that you need to match to the specifics of the universe that you're living in.

The effect that it has on the universe is that of a constant negative energy density. As you increase the size of the universe you have more and more volume which is filled with this negative energy density. It is very much unlike the normal matter or radiation that we are used to dealing with in that respect.

Lambda contributes to the curvature of the universe, but I do not believe that it can be regarded as a "true force."

Lambda is an intrinsic property of the structure of spacetime, a universe which had zero energy density and a lambda would expand exponentialy.

I don't think that's true. The strength of lambda's effect on the universe grows with the volume of the universe, but lambda itself isn't going to directly act on a particle. People draw analogies to coiled rubber sheets that, when you let go of them, want to expand out. In that sense you can think of lambda as an inheriant "stretchyness" of the spacetime structure.

I suppose so, it's a gravitational effect.

8. Feb 11, 2006

### pervect

Staff Emeritus
GR doesn't have "carrier particles". It only has curvature. So your question doesn't really work, it's a lot like the blind man asking if it is the trunk of the elephant that is the "true elephant", or the tail. The answer is that the trunk and tail are both part of the elephant.

Curvature and carrier particles are two different ways of describing the same entity, a "force".

In GR, we particularly study the trunk of the elephant (curvature), and leave studying the tail (carrier particles) to other disciplines.

Probably the best way to think about lambda is to think about empty space as having a slight negative "effective mass".

A more detailed explanation would say that space has a positive energy density, and a negative pressure, and that the energy density + 3 * pressure turns out to be a negative quantity. The quantity (density+3*pressure) is the "source term" for gravity, which is why I've called it "effective mass").

I can't quite recall offhand why density+3P acts as effictive mass - if space-time were static, it would be because that's the formula for Komar mass, but space-time isnt' static :-(. I think it may be a result of Birkhoff's theorem and isotropy (spherical isotropy).

Anwyay, this is probably getting too detailed, I hope that at least the general overview makes sense - empty space is hypothesized to contribute a repulsive term to gravity, the more empty space there is between two objects, the greater the relative acceleration induced.

We don't actually know that empty space has these properties - we don't have a detailed theory of quantum gravity to even calculate these properties (pressure and density) theoretically. Rather we assume that it (empty space) MIGHT have these properties, and point out that if it did, it would explain certain cosmological obsevations.