Why does my heart beat speed up and slow down?

It depends: Heart rate varies naturally with your breath. In some folks, it's really obvious & called "sinus arrhythmia" which is not harmful. With that, your pulse consistently slows when you breathe in and speeds up when you breath out. However, there is such a thing as "too fast" usually over 100 at rest, and "too slow", usually under 50 at rest. See your md if you are not sure.