We investigate a scenario in which neutrinos are coupled to a pseudoscalar degree of freedom \varphi and where decays \nu _ { 1 } \rightarrow \nu _ { 2 } + \varphi and inverse decays are the responsible mechanism for obtaining equilibrium .
In this context we discuss the implication of the invisible neutrino decay on the neutrino-pseudoscalar coupling constant and the neutrino lifetime .
Assuming the realistic scenario of a thermal background of neutrinos and pseudoscalar we update the bound on the ( off-diagonal ) neutrino-pseudoscalar coupling constant to g < 2.6 \times 10 ^ { -13 } and the bound on the neutrino lifetime to \tau < 1 \times 10 ^ { 13 } s .
Furthermore we confirm analytically that kinetic equilibrium is delayed by two Lorentz \gamma –factors – one for time dilation of the ( decaying ) neutrino lifetime and one from the opening angle .
We have also confirmed this behavior numerically .