Sachs-Wolfe effect in a Dark Energy universe?

[Suekdccia]

TL;DR

Sachs-Wolfe effect in Dark Energy universe?

The integrated Sachs-Wolfe effect occurs when a photon goes through a gravitational potential that changes due to spacetime expansion (presumably caused by dark energy). For that reason, a photon going through a gravitational well would gain energy (blueshift) when entering and it would lose energy (redshift) when exiting it. If the universe expands, the well becomes "less deep" and therefore, the photon gets more energy and becomes blueshifted.

However, would this effect still occur if we had a photon traveling in a universe with only one galaxy (the Milky Way) and the rest of it dominated by Dark Energy (that is, the Universe once the expansion separates all non-gravitationally bounded structures to us)?

 

[PeterDonis]

The integrated Sachs-Wolfe effect occurs when a photon goes through a gravitational potential that changes due to spacetime expansion

Yes.

(presumably caused by dark energy)

No. Dark energy is not the cause of expansion. It's only the cause of accelerated expansion. But you don't need accelerated expansion to have a nonzero integrated Sachs-Wolfe effect. All you need is some spatial variation in density.

would this effect still occur if we had a photon traveling in a universe with only one galaxy (the Milky Way) and the rest of it dominated by Dark Energy (that is, the Universe once the expansion separates all non-gravitationally bounded structures to us)?

If you postulate that there are no other gravity wells except the one we are in, then no, we would no longer observe any Sachs-Wolfe effect, just a (small) blueshift from photons falling into our gravity well.