- The civilization is in a galaxy which is not the Milky Way. For the purposes of this question, assume the target galaxy is 0.5 Mpc away.
- The civilization has elected, for whatever reason and regardless of practicality, to build full Dyson spheres. Assume for the purpose of the question that they had all the necessary mass within their galaxy to do this.
- The Dyson spheres absorb 100% of all energy emitted from the stars and do not emit any heat. From the perspective of our understanding of science, that's probably impossible, but for the purpose of the question, please assume it's true.
- The civilization has elected, for whatever reason and regardless of practicality, to enclose each and every energy-emitting source in their galaxy with the exception of black holes.
From a certain point of view, the galaxy is dark, with no visible-spectrum light emitted. This question does not embrace the effects of Dark Matter (we can't detect it today anyway). All the mass is there, but all the stellar-emitted light is gone.
It is my recommendation that unless you're absolutely sure about your answer that you give this question a half-day before answering for people to ask for clarifications. I'm expecting the requests.
Question: How could Earth, 2023, detect such a galaxy?
Do not worry about how long this might take. In other words, if it just so happens that some aspect of the James Webb telescope could do this, assume that serendipitously it just happened to sweep across the galaxy's location last night and explain how it succeeded.
I am not asking that we discover the presence of the Dyson spheres. I am only asking about detecting the presence of the galaxy. As in some lucky astronomer sending out a Tweet along the lines of, "we can't see it, but we know it's there, and we know it's the size of a galaxy."