4 problems

Gauge-invariant decomposition conjecture. There exist a tensor field ${\cal H}_{ab}$ and a vector field $X^a$ such that

No-backreaction conjecture. Standard perturbative approaches to cosmological perturbation theory implicitly conjecture that backreaction can be ignored.

Universal decomposition conjecture. The above assumption for the decomposition of the linear-order metric perturbation is correct for any background spacetime.

Let $X^{a}$ be a vector field constructed from some components of the linear-order metric perturbation, with gauge transformation rule given by the second equation in the linear me…