Depends on which phase of the expansion you are talking about. Right now, dark energy is the dominant energy contributor, so is what drives the expansion. At an earlier time, ordinary matter dominated and before that light energy dominated. In each case, the expansion is described nicely by general relativity applied to the way the energy density changes under expansion or contraction.
Oh, you want a 'cause' for the universe. Sorry, that makes no sense. All causality is *within* the universe. Causes only make sense when time exists and that is at or after after the BB.
Expansion and dark energy are both connected to the 2nd law. Astral Physics has the cause and affect backwards, when it tries to make dark energy lead.
One way to understand this is with a simple example. Say we have two factories that both make widgets. Both factories are exactly the same, with both creating X defects per day. I will use the defects to measure the relative entropy changes of both factories, since defects makes life more complicated for the Process Engineers; higher complexity situation to deal with.
Next, I will place one factory in each of two different space-time frames of reference, so I can see them for a side by side for comparison; compact versus expanded space-time references. One factory will placed in a more time dilated reference; compact universe, and the other in a less time dilated reference; expansion universe.
If we look at both factories, side by side, from an earth reference, the factory in the more expanded space-time reference will appear to make more defects per hour in our reference, since its time is moving faster. The other contracted reference with time slowed, appears to make fewer defect per hour, based on the same side by side comparison. Expansion amplifies the second law, and adds more defects per any standard reference of time. Expansion is consistent with the second law adding complexity.
When entropy increases, energy is absorbed; endothermic. The expansion, by increasing the rate of entropy will also increase the rate at which energy is absorbed from the universe; amplifying red shift. We see this an an accelerated expansion. I often wondered where the energy went during a red shift since the red shift lowers the energy value for all photons.
If I take two objects and bring them together, this will lower their complexity similar to a vapor becoming a liquid; fewer degrees of freedom. This reflects a loss of entropy and should be exothermic; heat of vaporization and blue shift. If I go from together back to separated; liquid to gas, this increases entropy and absorbs energy; endothermic or red shift. Galaxies that approach each other lower entropy; exothermic or blue shift. But most galaxies expand away from each other consist with the needs of the second law.
The 2nd law states that the entropy of the universe has to increase over time Therefore, one would expect more red shift than blue shift in our universe, which is seen. Entropy has to net increase, also implies the universe is bleeding energy, that goes into the ever increasing endothermic nature of entropy increase. This lost energy is conserved, as dark energy, but it is no longer part of the universe's useful free energy budget. We can see lost energy pockets all over the universe; called dark energy, which formed from entropy, acting upon matter and energy. Dark energy is a product of the universe.
Entropy is not energy, since free energy G = -TS, where T is temperature and S is entropy. Free energy is sort of an engineering term used to describe energy that you can easily exploited; free. The minus sign before TS implies the universe is always losing free energy; its easy to use energy, due to the constant entropy increase; available universal free energy decreases with time.
Entropy times temperature is energy. But entropy is not energy per se. At absolute zero, we have zero temperature; T=0, but entropy still exists. The energy value of entropy is a function of temperature; heat and energy, but entropy by itself, exists apart from energy; different but parallel realm we call dark matter and dark energy.
Life and the brain generates a lot of entropy; metabolism and neuron firing, with neurons firing connected to the action of our memory. Conceptually, the connection between memory and universal entropy increase, implies we are adding entropic content to the dark energy pool, based on our unique entropic memory signatures; endothermic. Science is now looking to see if dark energy interacts with itself; any organizing affects in the other realm.
We cannot see dark energy in the lab. The reason is there is no perpetual motion and all experiments will increase entropy and thereby add to the pool; data is lost but conserved. We can only see the larger scale universal scale affects. Since the pool of dark energy comes from the past, it acts like the inertia of where we came from, that impacts where we are heading.
The term entropy was first coined during the development of early steam engines. Engineers notice that there was lost energy that could not be accounted for. This lost energy was called entropy. Engineering continues to use the concept of entropy since it is needs this for energy balances when making practical things. Physics lost its way, since they do not have to make anything practical when exploring the unknown extremes. It could ignore entropy, until now, with the evidence of dark energy pools that seem to hold the universe together; anchored in the past.