High-order corrections to inflationary perturbation spectra in quantum gravity

We compute the inflationary perturbation spectra and the quantity r+8nT to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the theory R+R2+C2 with the fakeon prescription/projection for C2). The spectra are functions of the inflationary running coupling α (1/k) and satisfy the cosmic renormalization-group flow equations, which determine the tilts and the running coefficients. The tensor fluctuations receive contributions from the spin-2 fakeon χ μν at every order of the expansion in powers of α ∼ 1/115. The dependence of the scalar spectrum on the χ μν mass mχ, on the other hand, starts from the α2 corrections, which are handled perturbatively in the ratio mφ/mχ, where mφ is the inflaton mass. The predictions have theoretical errors ranging from α4∼10-8 to α3 ∼ 10-6. Nontrivial issues concerning the fakeon projection at higher orders are addressed.