  Neutrinos, as the anisotropic stress tensor, have a damping effect on the
tensor mode perturbation from inflation to the $ \Lambda$ dominated era. First,
we study the squared amplitude reduction for the wavelength entering the
horizon during radiation and matter-dominated phases in the negatively curved
de Sitter spacetime. Then, by comparing with other spatial spacetimes, $ K=0 $
and $K=1$, the highest difference between closed and open cases is seen in the
matter-dominated era. Thus, neutrinos can be added as another candidate for
determining the nature of space-time.
