# Cosmological constant or dark energy or vaccum denisty/energy/energy density

1. Dec 24, 2009

### edpell

Are these five names
cosmological constant, dark energy, vacuum density, vacuum energy, vacuum energy density
names for the same thing?

2. Dec 24, 2009

### mathman

There is experimental evidence that the expansion of the universe is accelerating. The theory behind this is called dark energy. In general relativity it is connected to the cosmological constant. So far it is essentially a mathematical description.

At this point, physicists are trying to find a physical basis. The vacuum energy is being considered as such a basis. Unfortunately when trying to quantify the relationship between vaccum energy and the cosmo. constant, there appears to be a discrepancy of about 120 orders of magnitude. The question remains open.

3. Dec 24, 2009

### edpell

thanks mathman (can't believe I just said that) can you give me a reference or link about the 120 order of magnitude mismatch for vacuum energy versus observed acceleration of expansion? Thank again mathman.

4. Dec 25, 2009

### mathman

From Wikipedia - I've highlighted the key point.

Main article: Cosmological constant
For more details on this topic, see Equation of state (cosmology).
The simplest explanation for dark energy is that it is simply the "cost of having space": that is, a volume of space has some intrinsic, fundamental energy. This is the cosmological constant, sometimes called Lambda (hence Lambda-CDM model) after the Greek letter Λ, the symbol used to mathematically represent this quantity. Since energy and mass are related by E = mc2, Einstein's theory of general relativity predicts that it will have a gravitational effect. It is sometimes called a vacuum energy because it is the energy density of empty vacuum. In fact, most theories of particle physics predict vacuum fluctuations that would give the vacuum this sort of energy. This is related to the Casimir Effect, in which there is a small suction into regions where virtual particles are geometrically inhibited from forming (e.g. between plates with tiny separation). The cosmological constant is estimated by cosmologists to be on the order of 10−29g/cm³, or about 10−120 in reduced Planck units. However, particle physics predicts a natural value of 1 in reduced Planck units, a large discrepancy which is still not explained.
The cosmological constant has negative pressure equal to its energy density and so causes the expansion of the universe to accelerate. The reason why a cosmological constant has negative pressure can be seen from classical thermodynamics; Energy must be lost from inside a container to do work on the container. A change in volume dV requires work done equal to a change of energy −p dV, where p is the pressure. But the amount of energy in a box of vacuum energy actually increases when the volume increases (dV is positive), because the energy is equal to ρV, where ρ (rho) is the energy density of the cosmological constant. Therefore, p is negative and, in fact, p = −ρ.

A major outstanding problem is that most quantum field theories predict a huge cosmological constant from the energy of the quantum vacuum, more than 100 orders of magnitude too large.[12] This would need to be cancelled almost, but not exactly, by an equally large term of the opposite sign. Some supersymmetric theories require a cosmological constant that is exactly zero, which does not help. The present scientific consensus amounts to extrapolating the empirical evidence where it is relevant to predictions, and fine-tuning theories until a more elegant solution is found. Technically, this amounts to checking theories against macroscopic observations. Unfortunately, as the known error-margin in the constant predicts the fate of the universe more than its present state, many such "deeper" questions remain unknown.

Another problem arises with inclusion of the cosmic constant in the standard model: i.e., the appearance of solutions with regions of discontinuities (see classification of discontinuities for three examples) at low matter density.[13] Discontinuity also affects the past sign of the pressure assigned to the cosmic constant, changing from the current negative pressure to attractive, as one looks back towards the early Universe. A systematic, model-independent evaluation of the supernovae data supporting inclusion of the cosmic constant in the standard model indicates these data suffer systematic error. The supernovae data are not overwhelming evidence for an accelerating Universe expansion which may be simply gliding.[14] A numerical evaluation of WMAP and supernovae data for evidence that our local group exists in a local void with poor matter density compared to other locations, uncovered possible conflict in the analysis used to support the cosmic constant.[15] These findings should be considered shortcomings of the standard model, but only when a term for vacuum energy is included.

In spite of its problems, the cosmological constant is in many respects the most economical solution to the problem of cosmic acceleration. One number successfully explains a multitude of observations. Thus, the current standard model of cosmology, the Lambda-CDM model, includes the cosmological constant as an essential feature.

5. Dec 26, 2009

### edpell

thank you.

does the Casimir effect give a value for the vacuum density? If so, which does it agree with?

is the vacuum density related to the evaporation rate of small black holes (i.e the more virtual particles the more radiation and likewise the less virtual particles the slower the evaporation rate?

6. Dec 26, 2009

### mathman

I'm sorry to disappoint you, but you've passed the limit of my knowledge of the subject. Note that I'm a mathematician not a physicist.

7. Dec 26, 2009

### Prathyush

No, I don't think so. as mathman said the vaccum density is really small hence, you need a really large volume(cosmic) to measure the effects of the vaccum density. While the casmir force itself is small and falls rapidly with distance. someone confirm please!

I am unaware of such a connection. What you mean by more virtual particles more the radiation.

8. Dec 27, 2009

### twofish-quant

No it doesn't. The Casimir effect is a simple experiment that illustrates that vacuum energy exists. It doesn't demonstrate in any obvious way how much vacuum energy exists.

One way of thinking about it is that suppose that there is amount X of vacuum energy. The cashmir effect is happens because you reduce the amount of vacuum energy by delta X. However the effect doesn't tell you what X was in the first place, and X can be positive, negative, or zero.

No. One way of thinking about it, is that quantum mechanics causes quantities to be "fuzzy". So if you ask "how many particles do I have in this box", the number is never "exactly zero" but rather "more or less zero." The "more or less zero" answer has some observable consequences.

Using the idea of virtual particles lets you do calculations with small black holes (which is what Hawking did), but it's something separate.

9. Dec 27, 2009

### Prathyush

Casmir effect can tell the amount of vaccum energy depending on the Force.
In fact
$$F=\frac{dE}{dx}$$

$$E=V\Lambda$$

$$F/A=\Lambda$$

The force per unit area excluding EM effects is infact the cosmological constant.

Measuring the force due to vacuum energy(negative) is not possible in terrestrial scales, and is dominated by the EM vacuum energy(positive). However it is observed in cosmic scales.
The measurement of the Casmir Force can tell if the vacuum energy contained $$\Lambda$$ is positive or negetive. But the values are beyond current experimental limits.

10. Dec 30, 2009