# Accelerating expansion and the Cosmological Constant

1. Apr 27, 2006

### Royce

Einstein’s Cosmological Constant was inserted into his General Relativity equations to make the universe static, neither expanding nor contracting, as most physicists believed it was at that time, as his equations showed that the universe is unstable and would eventually contract into a single mass. When Hubble discovered that the universe is expanding the Cosmological Constant was abandoned and Einstein called it the worst blunder of his career.
Now, however, it appears the expansion of the universe is accelerating rather than slowing down as it would be expected if the expansion was due solely to the original Big Bang model and being slowed down by the effect of gravity. Therefore Einstein’s cosmological constant is being reinserted into his equations to reflect this acceleration.
The question I have is what could be driving this accelerated expansion? What property of the universe could the cosmological constant be modeling?
It is possible that space-time has an inherent or intrinsic nature to be flat as it takes the force of gravity to warp or cause space-time to curve. The force of gravity is apparently overcoming the force making space-time non-warped, non-curved or flat in four dimensions., the force of flatness or cosmological force, if you will. We therefore have two forces working on space-time, gravity trying to pull space-time into a closed curve as into a spheroid or singularity and the cosmological constant trying to force it flat.
Assuming that the universe started as a singularity or black hole of some spherical finite dimension at the big bang, the universe would have been tightly compacted into a dimensionless point, a singularity or into a very tiny sphere. When the universe expanded and cooled enough for matter, mass and space-time to form, well after the period of inflation, the universe was still relatively small and space-time would have been tightly curved. The force generated by space-time trying to become flat would accelerate the rate of expansion beyond that of the initial impetus of the Big Bang rather than the force of gravity slowing it down as expected even if it was expanding at or beyond escape velocity . This is what we see today.
Does this mean that the universe will continue to expand forever until it becomes a flat, cold, dead, homogeneous universe? No not necessarily. It could be possible that once space-time expands to the point where its cosmological force is less than its force of gravity, the expansion would begin to slowdown and eventually begin contacting until the cosmological force again exceeded the force of gravity. There would be some overshoot as the velocity of contraction was bled off before the universe would again begin expanding. This could go on forever and the universe would be pulsing over eons of time, ringing like a bell, never stable nor static but in a constant state of flux.
But what if the velocity of expansion is greater than escape velocity with or without the cosmological force? Wouldn’t the universe simply continue to expand forever? If, as I assumed earlier, the universe started as a singularity or a black hole of some finite dimension then escape velocity would exceed the speed of light. That’s what makes it a black hole. Can the expansion of space-time itself exceed the velocity of light? I don’t think that it can. Even if it could, if the universe is expanding into the void, into nothing, eventually gravity will slow down the velocity of expansion once it exceeds the cosmological force. There is no place else for space-time or the universe to go and no matter how weak gravity becomes due to the distance involved it never becomes zero. Gravity will always have a value greater than zero and the universe will never be perfectly flat.

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2. Apr 27, 2006

### MathematicalPhysicist

i don't understand something which pops up a lot in the discussions in PF.

why do you consider spacetime as an independent entity (or background) which acts on masses? why don't consider spacetime as that which mach and other relativists think, as a coordinate system which depends on the masses as the coordinates in it?

3. Apr 27, 2006

### SpaceTiger

Staff Emeritus
I'm sure it doesn't answer all of your questions, but for the time being, take a look at the Review of Mainstream Cosmology. Post #82 reviews what we currently know about dark energy and the cosmological constant.

4. Apr 27, 2006

### hellfire

The known mechanism that can make space geometrically flat is an accelerated exponential expansion. It is postulated that this was the case during inflation. The universe underwent a phase of exponential expansion that made space nearly flat. Afterwards, the universe went through an epoch of radiation and matter dominance that drives the geometry away from flatness. Furthermore, you did correctly point out that the cosmologial constant will lead again to such an expansion making space again nearly flat. However, the analogies between both phases of exponential expansion seam to stop there. For the current accelerated expansion to have an end, the dominance of the cosmological constant must cease. This requires the current vacuum state to be metastable, something similar as during inflation with the inflaton. I fail to see how this could happen, because the postulated nature of the cosmological constant and the inflaton field is very different.

5. Apr 27, 2006

### Royce

I don't think that space time is an independent entity. I think space-time is a property of or a consequence, an effect, of mass. I do think that it is more than a mathematical coordinate system. I think of it a set of dimensions giving direction, location, movement and velocity to mass. Mass and space-time are an entangled system. One cannot exist without the other.

6. Apr 27, 2006

### SpaceTiger

Staff Emeritus
Are you referring to the ZPE? Are you really that confident that we understand the origin of the CC/dark energy?

7. Apr 28, 2006

### hellfire

I was asuming a scenario with the cosmological constant but not other kind of dark energy. The cosmological constant is introduced in general relativity as an additional term in the Einstein-Hilbert action and, therefore, it appears as the $\Lambda$ term in the "left hand side" of Einstein equations. By the way, I have never really understood the reason why it is usually associated a energy-momentum tensor to it. From this point of view the $\Lambda$ is a constant and invariant modification of the action of gravity, without taking into account any $T_{\mu\nu}$ that might vary in time or maybe decay from some metastable state to another. This is the background for my assertion you have quoted. You are right that we actually do not know anything about the cosmological constant and it is even more mysterious if one associates a $T_{\mu\nu}$ to it, but for me there is no obvious relation between both phases of exponential expansion.

Last edited: Apr 28, 2006
8. Apr 28, 2006

### SpaceTiger

Staff Emeritus
Both possibilities seem reasonable to me. As I understand it, the most general form of Einstein's equation, including $\Lambda$ on the left-hand side, satisfies both the strong and weak equivalence principle. On the other hand, we could associate an energy with the vacuum with $P=-\rho$ and get exactly the same effect. The ZPE of QFT makes the latter possibility seem plausible as well. Then, of course, quintessence and "phantom" dark energy fields are not out of the question.

Presumably, if we could construct a reasonable QFT with a ZPE that exactly satisfies the measured cosmological constant, that would be more appealing than an ad hoc modification of gravity. On the other hand, some have suggested to me that there's no reason that $\Lambda$ (on the left-hand side) should be zero and that such a modification is itself ad hoc. This, I think, has led some to suggest that the tiny value of $\Lambda$ is expected from the anthropic principle.

These theoretical degeneracies (along with the fine-tuning and coincidence problems) give me the general impression that we really have no idea what is going on.

9. Apr 28, 2006

### hellfire

Thanks, this clarifies that point and I agree. In my mind the term "cosmological constant" refers to the modification of gravity and "dark energy" (that may behave as a cosmological constant) to any other mechanism or field that causes accelerated expansion. This may not be the standard terminology.

Besides of this I have the impression that there may be some theoretical need to have some common explanation for both phases of accelerated expansion. See for example section 3.1 of Dark Energy: Mystery of the Millennium, by T. Padmanabhan. In my opinion this addresses at least part of the problems mentioned in the original post. The idea to unify both phases seams suggestive, but there are problems as I mentioned before. Moreover, the author of the paper does not propose any concrete solution to solve this problem. It remains to see if (and how) such an idea would have some influence on the hypotheses about the fate of the universe.

Last edited: Apr 28, 2006
10. Apr 28, 2006

### brahma

Yes, the universe can expand with superluminal speed. The following phd thesis is dedicated to this problem.

Fundamental Aspects of the Expansion of the Universe and Cosmic Horizons

http://arxiv.org/abs/astro-ph/0402278

11. Apr 28, 2006

### SpaceTiger

Staff Emeritus
Yeah, I'm not sure what's standard, but I've heard physicists talk about the ZPE as a "source" for the cosmological constant, so I usually lump that in with the modification of gravity you're describing. Quintessence and phantom energy are definitely distiniguished from the cosmological constant, since they don't produce the same effect on the universe.

12. Apr 28, 2006

### ratfink

Sorry to be pedantic here but when you state:
This is untrue.
Hubble showed that the wavelengths of characteristic lines in the spectra of photons emitted by distant galaxies had a longer wavelength on arrival than when they set off - and this 'stretching' was proportional to distance.
That is all.
He called them 'velocities for 'convenience'
When Zwicky showed that the same result could be explained by photons losing energy as they travelled along, Hubble said;
"Ratfink. it is redshift that i measure, and that is what i call them."
Hubble did not believe that redshift meant expansion.
I will keep quiet from now on.

13. Apr 28, 2006

### DrChinese

According to Lineweaver and Davis, inflation continues today and has never actually stopped entirely. We are moving away from much of the universe at speeds > c and gravity alone will never be strong enough to cause a future contraction.

14. Apr 28, 2006

### SpaceTiger

Staff Emeritus
Inflation generally refers to a period in the universe's history in which the scale factor was increasing exponentially. It's true that we are superluminally receding from much of the universe even now, but this is not what defines inflation. Because of dark energy, we may be approaching an era very similar to inflation in which the scale factor increases exponentially, but again, most people don't refer to it as "inflation".