Fair enough. Getting back to the question at hand: "Is it correct to give up the principle of the conservation of energy, when considering the expansion of the universe"?

You say Yes (I think).

I say No. In the real world (as opposed to mathematical world) the energy is conserved from the BB, as I stated previously. Energy is going to be diluted in an infinite universe, forever. No possibility of escape, UNLESS another dimension (low density, low energy, Brane) collides with our dimension in some far off future. This is the Orthodox view.

However, I am open to other views: The Static Einstein Universe, redshift illusion to accelerated expansion, etc. But you'll have to address many variables (not just the conservation of energy), and sell your idea, along with your equations. This will be extremely difficult, if not impossible to achieve. Good luck-you'll need it.