What is the source of Dark Energy?

In theories with dark energy, an energy density is just a property of space — even “empty” space devoid of matter and radiation. It’s closely related to Einstein’s old idea of a “cosmological constant”. Dark energy isn’t something material that comes from somewhere. As space expands, you simply get more dark energy because there is more volume; a dark energy density is just something all space has.

Modern physics concerns itself with mathematical models that explain physical observations. An energy density associated with pure space is just part of today’s cosmological models. It’s there, in a very precise and well-defined way, to explain the observational fact that the expansion of the universe is speeding up rather than slowing down.

From the point of view of the mathematics of General Relativity, it is an extremely simple and natural way to explain this fact. If this seems abstract, it isn’t any more abstract than, say, quantum field theories of particle physics.

As for violating the conservation of energy, that law cannot be consistently formulated for the universe as a whole. We can talk about the local conservation of energy, but not the global conservation of energy for the universe.

The question about the origin/increase of (dark) energy is a question of fundamental physics. Let's talk about the elephant in the room: The standard model does not include a fundamental physical understanding for dark energy. Dark energy instead is a place holder term for a type of energy with an assumed negative pressure to give it a repulsive effect. Dark energy has been adopted in the mathematical model of expansion (Friedmann equations) to bring it in line with an apparent acceleration of expansion. This leaves three fundamental possibilities: 1. The standard model is correct, yet we still need a complete theory of energy that includes dark energy. 2. The standard model is just wrong. 3. The standard model is wrong and a complete theory of energy will demonstrate the physics of expansion in a different way than the standard model. I have demonstrated recently a physical model for expansion that naturally includes dark energy. It is questionable whether dark energy can be explained under the standard model without new physics.