If you were to measure your pulse rate while in a spaceship moving away from the Sun at a speed close to the speed of light, you would find that it was

Your pulse rate will be the same as it was while you were on Earth.

Explanation:

Since you are on the ship, and you have the same speed with the ship, then, you'll observe your heart rate to be the same as your heart rate while you were on Earth. This is because there is no relative speed between you and the ship, since you're both on the same frame of reference.