Although by then the universe will be mostly dark energy, Dr. Krauss said, it will be undetectable unless astronomers want to follow the course of the occasional star that gets thrown out of the galaxy and is caught up in the dark cosmic current. But it would have to be followed for 10 billion years, he said — an experiment the National Science Foundation would be unlikely to finance.

“This is even weirder,” Dr. Krauss said. “Five billion years ago dark energy was unobservable; 100 billion years from now it will become invisible again.”

It turns out that you don’t actually need dark energy to be this pessimistic about the future, as Dr. Krauss and Dr. Scherrer point out. In 1987, George Ellis, a mathematician and astronomer at the University of Cape Town, in South Africa, and Tony Rothman, currently lecturing at Princeton, wrote a paper showing how even ordinary expansion would gradually carry most galaxies too far away to be seen, setting the stage for cosmic ignorance.

Dark energy speeds up the picture, Dr. Ellis said in an e-mail message, adding that he was glad to see the new paper, which adds many astrophysical details. “It’s an interesting gloss on the far future,” he said.

James Peebles, a Princeton cosmologist, said there were more pressing worries. We might be headed toward a universe that is “asymptotically empty,” he said, “But I have the uneasy feeling that the U.S.A. is headed into asymptotic futility well before that.”

You might object that the inhabitants of the far future will be far more advanced than we are. Maybe they will be able to detect dark energy — or the extra dimensions of string theory, for that matter — in the laboratory. Maybe they will even be us, in some form or other, if the human race manages to get out of the solar system before the Sun blows up in five billion years. But if relativity is right, they won’t be able to build telescopes that can see past the edge of the universe.

It’s not too late to start thinking about sending out the robot probes that could drift down through alien skies eons from now with, if not us or our DNA, at least a few nuggets of wisdom — that the world is made of atoms and that it started with a bang.