  Neutrino mixing lead to a non zero contribution to the cosmological constant.
We consider non renormalization $1/M_{x}$ interaction term as a perturbation of
the neutrino mass matrix. We find that for the degenerate neutrino mass
spectrum. We assume that the neutrino masses and mixing arise through physics
at a scale intermediate between Planck Scale and the electroweak scale. We also
assume, above the electroweak breaking scale, neutrino masses are nearly
degenerate and their mixing is bimaximal. Quantum gravitational (Planck scale
)effects lead to an effective $SU(2)_{L}\times U(1)$ invariant dimension-5
Lagrangian involving neutrino and Higgs fields, which gives rise to additional
terms in neutrino mass matrix. There additional term can be considered to be
perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that
the gravitational interaction is flavour blind and we study the neutrino mixing
and cosmological constant due to physics above the GUT scale.
