Invariance of cosmological number counts under disformal transformations

We investigate whether true physical observables associated with the measurements of large scale structure in the universe are frame-independent. In particular, we study if cosmological observables such as the galaxy number counts are invariant under the disformal transformations. In a previous work, it was shown that this frame-invariance holds true for the case of conformal transformations. In this work, we find that the invariance also holds true for the case of a simple disformal transformation. We further briefly comment on the disformal invariance of other cosmological observables.