As the universe expands photons get stretched thus they have lower energy. So where does that energy go? How is energy conserved?

Disclaimer: I don’t have the math or physics knowledge to handle quantitative general relativity. So this is strictly my qualitative take, based on my understanding of how general relativity works.

The energy doesn’t “go” anywhere.

As the universe expands, space is stretched. That means that more void is created, and everything in the universe – both mass and energy – is spread more and more thinly on the void, subject only to the constraints of gravity.

So the energy of a photon simply spreads out. It doesn’t get less, it only gets less concentrated.

The situation is analogous to what happens when you plunge a chunk of red-hot steel into a bucket of water. The heat energy doesn’t “go” anywhere in the sense of vanishing; it just spreads out from the chunk of steel into the water. The weighted average temperature of the steel plus the water doesn’t fall, but the temperature of the steel certainly falls.

Now the universe is like this: imagine that the chunk of red-hot steel is plunged into an infinitely-large, perfectly insulated bucket that is gradually filling with water at absolute zero (no heat energy). The total heat energy in the bucket came from the chunk of steel, and it doesn’t decrease, but as more and more water is added (forever!) the heat gets more and more spread out, until the temperature of the water plus the steel approaches absolute zero. Eventually it will approach absolute zero as closely as you like, but the heat energy isn’t gone. It’s just spread out over a volume approaching infinity.

In the same way, a photon of light traveling for a very long time through an expanding universe gets stretched or smeared over a greater and greater volume. We see that as a redshift, as the photon being reduced in energy. What has actually happened is that the photon’s energy has been diluted by the expansion of the universe.

Dan Berger