If we define X = √Qs-ℛ and plugging it into Eq. (7.80View Equation), we obtain the perturbed action for the field X after the partial integration:
∫ [ ] (2) 3 ∘ --(0) 1 ˙2 1 1- 2 1 2 2 δS = dtd x − g 2X − 2 a2(∇X ) − 2M sX ,
where ∘ −-g(0) = a3 and M s is defined in Eq. (7.82View Equation). Then, for the field X, we obtain the Klein–Gordon equation □X = M 2X s in the large-scale limit (k → 0), which defines the mass M s in an invariant way in the FLRW background.