# Rate of expansion of the universe

1. Jun 11, 2014

### TonyB178

So I know that the rate of expansion of the universe is increasing, i.e. the 2nd time derivative of the size of the universe is positive. But, is the next time derivative (i.e. 3nd time derivative of the size of the universe) positive of negative? Do we have enough information to determine this? And lastly would a negative value indicate that eventually the expansion of the universe at some point in the future start slowing down, lead the rate of expansion to slow down and eventually become negative, and allow the possibility of a contracting universe in the very very very distant future?

A theoretical example (of a negative value of my above question) would be if spacetime cannot be infinitely stretched, and acts somewhat like a spring with some optimum amount of being stretched. We would still be in the "over-compressed" stage, and the extensive force causes the spring to accelerate back to it equilibrium position, but that amount of acceleration would be less and less as the spring approached its equilibrium position. Then at some point the spring passes through its equilibrium position , and a tensional force takes over to prevent further expansion. This creates a cycle (with period in the order of billions and billions of years, we would still be in the first half cycle) that could repeat infinitely (if no energy is lost per cycle) or which would decay in amplitude every cycle and eventually settle into the equilibrium position. spacetime would be a logical 3D (or 4D) extension of this scenario.

I know these ideas can't be proven, I'm just wondering if they could in theory be possible.

Last edited: Jun 11, 2014
2. Jun 11, 2014

### Mordred

yes the universe is expanding, I have no idea which equation your looking at in terms of derivitive's

however expansion is described by the FLRW metric and equivalently the Einstein field equations however these are not the only equations that can be used (see loop quantum cosmology)

the commonly used FLRW metric is used extensively in the lambdaCDM model $$\Lambda CDM$$ this is essentially a 6 parameter model, that describes the hot big bang model with cold dark matter and the cosmological constant.

fundamentally the model describes the universe in terms of a perfect fluid or ideal gas. matter,(including dark matter) and radiation, have a positive pressure influence. the cosmological constant has a negative pressure influence. (the energy density of each contributor has a corresponding energy-density to pressure relation) determined by its equation of state

http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

the cosmological constant ( dark energy as a possibility) is represented by $$\Lambda$$

the relation between the positive pressure contributors (matter both relativistic and non relativistic) and the cosmological constant (negative pressure contributor) determine the rate of expansion.

today the cosmological constant is the dominant contributor to expansion. In order for the universe to contract matter (gravity) would have to increase enough to overcome the cosmological constant.

Now space itself is not a fabric that is stretched, so your spring example is useless,

space is simply geometric volume that is filled with the contents of the universe. see this recent post for more info

3. Jun 12, 2014

### bapowell

No. The 'jerk' of the scale factor is very difficult to measure. See http://arxiv.org/abs/gr-qc/0309109.

4. Jun 12, 2014

### TonyB178

Thanks bapowell, the "jerk" of the scale factor is exactly what I was referring to. I had suspected we couldn't accurately measure it (yet), but I wasn't sure.

I personally am a geophysiscist and while i look into cosmology and other areas of physics for fun and to better my understanding of the universe, but this is not my area of expertise. That being said, if my education has taught me one thing its that the terms "ideal gas", "perfect fluid", "isotropic", "homogeneous", etc. are almost always an approximation and wrong to some degree or another. I think this is especially true in cosmology, considering 95% of the universe (dark matter and dark energy) is barely understood at all and only perceived through gravitational lensing and accelerating expansion of the universe and other second-hand observations. SO, do we really know that our current equations that are based on assumptions such as space being an isotropic and perfect fluid and the cosmological constant being spatially and temporally constant are actually valid?

5. Jun 12, 2014

### Chalnoth

I am always annoyed at this comparison. The 95% figure is a very arbitrary measure of knowledge: it is largely a result of the specific time that we happen to live in. If you did the same comparison in the early universe, baryonic matter would make up 16% of the universe's energy density and dark matter would make up nearly all of the remaining 84%. Go even earlier, and essentially the entire energy density of the universe would be made of radiation, which we ostensibly know quite a lot about.

Furthermore, even if dark matter makes up more than five times as much of the energy density of our universe, does that really mean that we would understand five times more stuff if we understood dark matter? What if dark matter is only made up of a single particle? Would understanding the nature of that particle really expand our understanding of physics by that much? Probably not.

As far as fundamental laws are concerned, we currently know all of the fundamental laws that are required to understand the physics of every-day life. We probably also know the fundamental laws that are necessary to understand all future technologies for decades if not centuries into the future. Now, those laws that we do know are exceedingly complex and we certainly have far to go in investigating all of the various ways that those laws can be put to use to produce interesting things. But I don't think we'll need anything beyond the standard model of physics plus general relativity for a long, long time to describe the behavior of technology.

In other words, we really know a lot about how the universe works.