How do dark energy and the law of conservation of energy fit together?

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The law of conservation of energy is one of the fundamental laws of the Universe, it has been experimentally confirmed countless times and it will not work to violate it, no matter how much you want.

If one gets the impression that in some process the law of conservation of energy is violated, this means that some nuance has been missed. Dark energy makes galaxies scatter, which means it gives them kinetic energy, which, at first glance, comes from nowhere, but this is not so.

Before the Big Bang, the universe did not exist, which means that its energy was zero, so the total energy of the universe must always be zero and it is impossible to add something to it.

The fact is that, according to theoretical calculations, there is a so-called anti-energy. At the moment of the Big Bang, anti-energy formed space, and ordinary energy filled it and soon formed matter.

With the expansion of the universe, the volume of space is constantly growing, which means that the amount of anti-energy also increases, which is compensated by an increase in the speed of galaxies and, accordingly, their kinetic energy. Therefore, with the conservation of energy during the expansion of the universe, everything is in order and dark energy does not violate it in any way.