I'm trying to remember the name of this book, by a classical american author. In the 21th or 22th century, a physics effect is discovered which allows travel at the speed of light. Some time after, observations shows traces of aliens having traveled, using this effect, and a ship is sent to the alien home world. When this world is reached, the aliens tell them that they suspect that traveling at light speed "unravels the fabric of the universe" and increases the probability of the universe ending because of a jump to a different quantum state (false vacuum?) or something like that. So they have abandoned space travel. The ship returns to Earth where many years have passed and the society is a static one. Then they go on to a colony on a nearby star. At the end they discover that space travel increases and not decreases the stability of the universe.
I believe this is Starfarers, first published in 1998.
Earth sends out a spaceship to investigate starfaring in far distances of which traces have been found. The ship ENVOY manned by a crew of six men and four women travels at speed close to the speed of light. At least so close, that a few years ship time mean ten thousand years passing back on earth. The traveling method is Zero-Zero-Jumps taking Energy from the substrate of space. As captain Nansen's ship travels further into space, but still inside the milky way, traces of spacefaring disappear. The big question is, why does spacefaring stop? --- Edited from Wikipedia