Perturbative algebraic quantum field theory on the DFR spacetime and cosmological perturbations (2024)
In this work, a new construction of the original proposal of the Doplicher-Fredehagen-Roberts (DFR) model of a quantum spacetime is presented in the framework of perturbative Algebraic Quantum Field Theory (pAQFT) as a non-local effective Quantum Field Theory (QFT), which we call Moyal type, and it is compared with the Quantum Diagonal Map. Thereafter, the time (T) and retarded (R) products in the interacting QFT are obtained, and the singularity structure of the resulting distributions is analyzed using tools of microlocal analysis. Then, after an extensive review of QFT on curved backgrounds, a proposal to introduce the noncommutative effects of the DFR spacetime in a cosmological background is presented, resulting on non-local effects in diffeomerphism invariant linear cosmological perturbations besides the already known nonlocality of the Bardeen potentials.