If we could slow the speed of astronauts below the speed of Earth-bound humans those astronauts will live faster and will produce science faster than those on Earth, so on their return we could learn from them.
But, how to slow down your speed when you can only measure your relative speed?

Interesting idea, but I think you have some basic misunderstandings of how relativity works. Under special relativity when two bodies are moving at a constant velocity relative to each other each will perceive that the other's clock is running slow. Neither perceive's that the other's clock is running fast.

But under general relativity in which one body is being accelerated the assymetry of the situation has a profound effect. If an astronaut departs earth and later returns he would have aged slower than his counterparts on earth. To him time on earth seems speeded up. So to answer your question - to produce science faster for the general population what you need to do is load the population onto a giant spaceship, but leave all the scientists and engineers behind on earth. Then set a course for Alpha Centauri and back at close to the speed of light. When the people return they will have aged perhaps 5 years, but meanwhile 10 years would have passed on earth. So after a 5 year trip the people get to enjoy the scientific advances of 10 years!