Source of Dark Energy. In accelerated expansion dark energy play a crucial role because of negative pressure, but during expansion Dark Energy(DE) do not dilute. DE density is independent of scale factor unlike matter and radiation energy densities, which decrease with expansion.
What is the source of this dark energy and why it do not decrese in universe expansion.
 A: I think there is no common explanation for this. Some people try to build some theories about that, but nobody can prove them. Every "beyond standard model" theory probably has it's own explanation for dark energy.
One of them is still pretty interesting at least. I remember that Stanley Brodsky talked about that during the NED/TURIC meeting in 2014. He uses a formalism based on holographic principle and light front formalism (which is quite complicated for me to understand) in which he has a theory about the vacuum of qcd. He uses it as an explanation for dark energy.
https://www.slac.stanford.edu/th/lectures/Stanford_DarkEnergy_B_Dec2010.pdf
The idea is that the pairs of quark condensate lies in hadrons (like proton, neutron ...) and not in the vacuum. This lecture is really the beginning as lots of complicated tools are not presented here (like AdS/QCD) but you might find it interesting.
A: The FLRW energy equation 
$$
\left(\frac{\dot a}{a}\right)^2~=~\frac{8\pi G\rho}{3c^2}
$$
gives a solution for the scale factor $a(t)~=~a_0(t)exp(t~\sqrt{\frac{8\pi G\rho}{3c^2}})$. We have here that the density $\rho$ is the density of energy in the vacuum of space. This is most often thought of as due to the zero point energy of quantum mechanics. The difficulty comes when one realizes that the sum over vacuum modes $\frac{1}{2}\sum_n \hbar\omega(n)$ is a very large number. It is infinite if one sum to infinite frequency and very large if one sums up to the Planck energy. The energy density predicted would then be $\rho~\sim~E_{zpe}^2$ $\sim~10^{76}GeV^4$ that predicts a comsological constant in length units $10^{70}m^{-2}$, and the measured cosmological constant
$$
\Lambda~-~ \frac{8\pi G\rho}{c^2}
$$
is $\Lambda~=~10^{-52}m^{-2}$. This is a scaling difference of $122$ orders of magnitude difference!
The negative pressure comes into the picture with the $\rho~+~wp~=~0$ condition on the elements of the stress-energy. This requires that $w~=~-1$ and that the sign on the pressure is negative.
How does one get around this? One argument for supersymmetry has been that boson vacuum modes are matched by SUSY paired fermionic modes with negative energy. We then have that the energy of the vacuum is naturally zero. There is a problem here, this might work for the Lagrangian but not for the vacuum. SUSY is broken and the vacuum does not have at low energy the symmetries of the Lagrangian. This also only buys you much if SUSY breaks at rather low energy. The data coming out of LHC is threatening us with the prospect that low energy SUSY, or so called low mass SUSY particles, is not not how nature works. A lot of particle physics phenomenology is threatened with being sent to the shredder.
't Hooft and Nobbenhuis   have an interesting idea that is a type of Wick rotation on QM that results in commutator terms that counter the standard QM commutators. I am not aware of how far this has gotten, and it seems to have not gained much traction.
The papers referenced by JSFDude are interesting and similar to something I proposed 15 years ago. I said that maybe there is some condensate physics of quarks in hadrons that is analogous to superconductivity. In this setting the hadron has a sort of Meissner effect with respect to the exterior vacuum. This would be a sort of negative pressure, and it could be some aspect to dark energy.
Quick comment. The light front formalism of physics can be seen in the invariant 4 momentum
$$
m^2~=~E^2~-~(p_x^2~+~p_y^2~+~-p_z^2)
$$
Let us assume this system is highly boosted along the $z$ axis. This means that $p_z~>>~p_x,~p_y$ and that we could write the energy $E$ as
$$
E~=~\sqrt{p_x^2~+~p_y^2~+~p_z^2~+~m^2}~=~p_z\sqrt{1~+~\frac{p_y^2~+~p_z^2~+~m^2}{p_z}}~\simeq~p_z~+~\frac{1}{2}p_z^{-1}(p_x^2~+~p_y^2~+~m^2)
$$
This then leads to a nonrelativistic form 
$$
\frac{E~-~p_z}{p_z}~=~\frac{1}{2}(p_x^2~+~p_y^2~+~m^2).
$$
This in the limit of infinite Lorentz boost puts the system on the light front. The apparent nonrelativistic form of this is due to the time dilation that occurs which apparently slows down motion along the other directions. 
A: The question about the origin/source of dark energy is a key question of fundamental physics. The standard model does not include a fundamental physical understanding of dark energy. The term has been adopted in the mathematical model of expansion (Friedmann equations) to bring the model quantitatively in line with the observation of an apparent acceleration of expansion. Without an understanding of what dark energy is and how it arises the fundamental physics of expansion are not understood. The theory of energy is incomplete. Some suggestions have been published that suggest the presence of negative energy. However, negative energy is outside the Lambda-CDM model and proof has been considered the issue. A direct proof for negative energy based on a specific mechanism for its source has been suggested here.
