  We start from the assumption that the theory of gravity can be formulated in
terms of 4-dimensional action, and there are only 2 graviton polarization
states, as in general relativity. It can be a non-perturbative effective action
discussed in the asymptotic safety program or the result of some other UV
modification of the general relativity making it a complete theory. From these
general grounds, we study the properties of the graviton two-point function on
top of cosmological de-Sitter space. We find that the no-ghost requirement
formulated for the flat background does not necessarily hold for the de-Sitter
space where the graviton two-point function can have an infinite number of
complex-conjugate poles. We show that under certain stability conditions, their
appearance doesn't contradict any fundamental principle. We discuss their
observational consequences for the tensor power spectrum from inflation and for
the stochastic gravitational wave background.
