  In this work we have analysed some cosmological bounds concerning an open
FLRW solution of massive gravity. The constraints with recent observational
$H(z)$ data were found and the best fit values for the cosmological parameters
are in agreement with the $\Lambda$CDM model, and also point to a nearly open
spatial curvature, as expected from the model. The graviton mass dependence
with the constant parameters $\alpha_3$ and $\alpha_4$, related to the
additional lagrangians terms of the model, are also analysed, and we have
obtained a strong dependence with such parameters, although the condition
$m_g\simeq H_0^{-1}$ seems dominant for a long range of the parameters
$\alpha_3$ and $\alpha_4$.
