Background-induced complex mass states of graviton: quantization and tensor power spectrum

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.