What is the significance of the cosmological jerk in the expanding universe?

[Ontophobe]

The expansion of the universe is in a state of perpetual acceleration as evidenced by the cosmological redshift. But is there a jerk to this acceleration? Is the acceleration of the universe's expansion itself speeding up, staying the same, or slowing down?

 

[Chronos]

For discussion, see http://arxiv.org/abs/1601.05172, A parametric reconstruction of the cosmological jerk from diverse observational data sets. For a general treatment of the question, there is http://arxiv.org/abs/0807.0207, Cosmic Jerk, Snap and Beyond. It is a very difficult thing to measure, so the answer is uncertain at present. It is, however, an interesting question because a definitive answer could rule out [or allow] any number of cosmological models, as mentioned in the referenced papers.

 

[Chalnoth]

The expansion of the universe is in a state of perpetual acceleration as evidenced by the cosmological redshift. But is there a jerk to this acceleration? Is the acceleration of the universe's expansion itself speeding up, staying the same, or slowing down?

The rate of expansion is slowing down. If the rate of expansion were to increase in the future, that would require an exceedingly surprising modification of physics.

The expansion is called an accelerated expansion because the distances between far-away objects is currently increasing at an accelerating pace. This is because while the rate is slowing, it appears to be approaching a constant. With a constant rate of expansion, we can calculate how the scale factor changes as follows:

$$H(t) = {1 \over a(t)} {da \over dt} = H_0$$
$${da \over dt} = H_0 a$$

The solution to the above differential equation is $a(t) = a(0) e^{H_0 t}$. That is, if the rate of expansion is a constant, then the distances between objects is represented by exponential growth. With exponential growth, then the functional form of all derivatives is the same: an exponential that scales as $e^{H_0 t}$, just with a different power of $H_0$ in front (e.g. the acceleration is $H_0^2 e^{H_0 t}$, the jerk is $H_0^3 e^{H_0 t}$, etc.).

 

[JonnyG]

This is because while the rate is slowing, it appears to be approaching a constant.

Doesn't this rule out a spherical geometry of space? Also, if we are able to determine this constant then should we not be able to determine if space is flat or hyperbolic?

 

[Chalnoth]

Doesn't this rule out a spherical geometry of space? Also, if we are able to determine this constant then should we not be able to determine if space is flat or hyperbolic?

Having a spherical geometry is unrelated to this question. The kind of expansion I described in the above occurs whenever you have a positive cosmological constant and wait long enough that the matter density is much lower than the cosmological constant.

 

[Fervent Freyja]

For discussion, see http://arxiv.org/abs/1601.05172, A parametric reconstruction of the cosmological jerk from diverse observational data sets. For a general treatment of the question, there is http://arxiv.org/abs/0807.0207, Cosmic Jerk, Snap and Beyond. It is a very difficult thing to measure, so the answer is uncertain at present. It is, however, an interesting question because a definitive answer could rule out [or allow] any number of cosmological models, as mentioned in the referenced papers.

OMG, I'm so excited with these papers right now, I've printed them out and they will make laundry & cleaning day today much better- thank you, thank you, thank you! This is why I love PF! Do you have any more links on the topic? Where is a dancing smilie?