acceleration of the universe Moments after the Big Bang, the universe was expanding at an incredible rate, (I've heard) faster than the speed of light. Due to dark energy, scientists predict the rate of expansion will pick up again. Space itself will be expanding faster than light speed. Someday, we will not be able to see other galaxies because they'll be moving away so fast that the light they produce will never reach us. Nowadays, though, we can see other galaxies, which means the expansion of the universe slowed down.
What caused the expansion of the universe to accelerate more slowly? If dark energy is causing the acceleration to increase, wouldn't the universe continue to expand faster after the big bang?
Is there a minimum rate of acceleration? If so, what is it, and what determines it?
 A: There is not a minimum rate of acceleration. In fact, before the discovery of dark energy most people thought that the universe would deccelerate. That is still a mathematical possibility - if dark energy is not a cosmological constant and its equation of state changes in the future.
The vast difference in scale between the early inflation and present day expansion is explained by the fact that it is thought that the early inflation and current acceleration have different causes. If there is a common cause then there must be some bizarre dynamics going on to connect things across many orders of magnitude that is not at all likely according to theoretical prejudice.
The expansion of the universe (in the approximation where you can ignore the fact that the universe isn't perfectly uniform) is governed by the Friedmann equation:
$$ \left( \frac{\dot{a}}{a} \right)^2 = \frac{8\pi G}{3} \rho - \frac{k}{a^2} + \frac{\Lambda}{3} $$
(units where $c=1$) where the scale factor $a$ measures the size of the universe, $\rho$ is the energy density, $k$ measures the curvature of space and $\Lambda$ is the cosmological constant. $G$ is Newton's gravitational constant. For all practical purposes $k$ is zero in our universe.
Now in order to find how the universe expands you need to know how the energy density changes with scale factor. There are some common cases:


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*Matter: $\rho \propto a^{-3}$

*Radiation: $\rho \propto a^{-4}$

*Vacuum energy (slow rolling scalar field): $\rho \propto a^0$
If you plug these in and work things out you will find that when matter and radiation dominate the expansion is slowing down, but when vacuum energy or $\Lambda$ dominates the expansion speeds up. (The critical point, i.e. steady non-accelerating expansion, is for $\rho \propto a^{-2}$, which corresponds to a gas of cosmic strings, I think, but need to confirm this.) So you can get the proposed expansion history from the following standard scenario:


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*The universe starts in a state dominated by a slow rolling scalar field (inflaton) with a large energy density $\rho\sim\text{constant}$. This drives a rapid and accelerating expansion.

*At some point the scalar field hits a phase transition and its energy is converted into ordinary matter and radiation. This is called reheating.

*While radiation and, subsequently, matter dominate the energy density of the universe the expansion continues but slows down.

*Eventually the radiation and matter dilute away to the point that the cosmological constant (or dark energy) dominate the energy density. At this point the expansion starts speeding up again. This happened about a billion years ago in our universe. The pattern is very similar to inflation in step 1, but the scale of the energy density is many orders of magnitude smaller, which is why it took so long for the change over to take place.

*If the expansion is really being driven by a cosmological constant then this acceleration will continue forever. If, on the other hand, it is being driven by some more complicated dark energy mechanism then there are many possibilities for the future...
