BW : we hope not. Some humans use excessive energy to travel faster thsn they should (it is better to travel than to arrive), and the planet's resources, purity are ruined by it.
So humans remain on Earth until it dies or human race wiped out? Concerned about the 'universes' resources? Have you even a concept of how big the universe is? TRILLIONS of planets, how long do you think it will take humans to deplete the universes resources? Plus light speed makes it instantaneous for humans but not for time, the planet, or whoever is not traveling at light speed. So if went to a planet 1 million light years away, it wouldn't make humans instantly there and we are instantly at all planets, those who are not traveling, the time still goes by. So 1 million years would pass for a human to go to a planet 1 million light years away, but for that human it only feels instantaneous.
But soon will come means many consider unethical to control human population, and will need to have the ability to spread to other planets. Eventually Earth will die, or the sun will.