Shear viscosity in a superfluid cold Fermi gas at unitarity

We analyze the contributions of Nambu-Goldstone modes to the shear viscosity of a superfluid atomic Fermi gas close to unitarity. We show that the low temperature experimental values of the shear viscosity to entropy ratio, $\eta/s$, are reproduced considering an effective shear viscosity which takes into account the collisions among Nambu-Goldstone bosons and the finite size of the optical trap. We predict that, for $T \lesssim 0.1 T_F$, $\eta/s$ should correlate with the size of the trap and linearly decrease with decreasing temperature. For $T \gtrsim 0.1 T_F$, we find agreement with the experimental data assuming that the Nambu-Goldstone modes have an anomalous dispersion law.