Welcome to PF!
As mathman also pointed out, I think you're confusing dark matter with dark energy. Despite the names, they are in no way related. That is a misnomer.
So, I'm guessing your question is about dark energy- so I'll address that. Dark energy is the umbrella term for whatever causes the acceleration of expansion. NOT expansion itself. It was known the universe is expanding since 1929.
Fluids in cosmology have an equation of state - a quantity given by w = p/ \rho, where p is the pressure, and \rho is its energy density. For anything that is accelerating the universe, then w < - \frac {1} {3} must be true. Note that this quantity is negative, because dark energy must have a negative pressure. In the FLRW metric, negative pressures can drive the acceleration of the universe if it is already expanding.
So, with this information, there are a few candidates:
Cosmological Constant (CC): Note that, first of all, this is also known as 'vacuum energy'. They are the same thing. In the Einstein Field Equations, there is a term, \Lambda, that refers to a sort of vacuum energy - an energy that just comes with space, you can't get rid of it. Einstein introduced the CC after Alexander Friedman showed him that general relativity requires that the universe must be expanding. However, Einstein's CC was negative, it would counteract the effects of expansion to keep the universe static. After it was shown the universe was expanding, interest in the CC was lost. However, after the discovery of dark energy, interest in it has been renewed. The most important property of the CC is the fact it is constant - it will remain the same forever, keeping the universe accelerating until it suffers heat death. For the CC, w = -1. That is unchanging. If there is a CC, it's density would be \Omega_{ \Lambda } \simeq \frac {2} {3}, keep in mind this remains constant for eternity. In terms of Planck units, its value is astronomically low - about ~10-120. Quantum mechanics also predicts a type of vacuum energy, and it was hoped the value of this would meet the CC. However, it disagrees by a factor of 100 orders of magnitude.
Quintessence (Q) - Q would be a dynamical field that can change over time. W would be w = \frac{\frac{1}{2}Q^{2}-V(Q)} {\frac{1}{2}Q^{2}+V(Q)}
Theories of Q vary, so I don't really know where to start. But one case includes a Q known as 'phantom energy'. Phantom energy would have a w < -1, so acceleration would be non-constant. This would lead to a 'Big Rip' scenario, in which expansion accelerates until everything is pulled to pieces.
Of course, it could be none of these. But, I would lean towards a cosmological constant. Measurements of the equation of state in the future will be the best judge.
