The luminosity and the radius of the star increase. Only The Core Contracts. The surface temperature of the star drops. Thus the star appears bigger and redder. After its large increase in luminosity while ascending the red-giant branch is terminated by the helium flash, our star settles down into another equilibrium state at stage 10, on the horizontal branch.
Some cool physics occurs in the core as it is being compressed by gravity.
As material is squeezed ever tighter together is stops and acting like an ordinary gas. The spacing between atoms gets close enough that quantum effects become important. The gas is called a degenerate gas . The Pauli - Exclusion Principle. No two particles can occupy the same state at the same time.