High-order corrections to inflationary perturbation spectra in quantum gravity

We compute the inflationary perturbation spectra and quantity r+8nT to next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means theory R+R2+C2 fakeon prescription/projection for C2). The are functions of running coupling ? (1/k) satisfy cosmic renormalization-group flow equations, which determine tilts coefficients. tensor fluctuations receive contributions from spin-2 ? ?? at every expansion powers ? 1/115. dependence scalar spectrum on mass m?, other hand, starts ?2 corrections, handled perturbatively ratio m?/m?, where m? is inflaton mass. predictions have theoretical errors ranging ?4?10?8 ?3 10?6. Nontrivial issues concerning projection higher orders addressed.