Which substance is responsible for the red color in red algae? carotenoids chlorophyll fucoxanthin phycoerythrin

The answer is phycoerythrin.

Red algae are red because they have pigment phycoerythrin. Red algae live in much deeper water than green algae. It is known that chlorophyll absorbs red light and reflects green. That's why plants containing chlorophyll are green. At a depth of the sea where red algae live, there is no red light but blue light. Phycoerythrin absorbs that blue light and reflects red giving the red algae red color. So, phycoerythrin allows red algae to photosynthesize and live in greater depths than the other algae.