Question

Why is the entropy of universe constant

Answer 1

When this heat death is reached, the Universe will attain a thermodynamic equilibrium and will have maximum entropy (which will essentially be constant). It is common to hear in cosmology that the entropy of the universe is adiabatic (constant) at late times

Answer 2

If we think the whole Universe as a closed system, then the entropy must be constant,according to quantum mechanics. The whole process is reversible, entropy change should be zero. It means that the total entropy of the universe can be constant.