Final answer:
The arrector pili are tiny muscles in the dermis that contract due to stimuli from the sympathetic nervous system, causing hair to stand up and create goose bumps when a person is cold or frightened.
Step-by-step explanation:
The muscle that causes goose bumps when a person is frightened or cold is the arrector pili. These tiny muscles are located in the dermis, the layer of skin below the epidermis. When a person is cold or experiences an emotional reaction like fear, the sympathetic nervous system triggers these muscles to contract. This pulls on the hair follicles, causing the hair to stand up straight and result in the characteristic bumps on the skin known as goose bumps. This involuntary reaction is similar to the reflex that causes shivering, which also involves muscles but primarily skeletal muscles that are stimulated to release heat energy and elevate body temperature.