High-order corrections to inflationary perturbation spectra in quantum gravity

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

Automated summary

In this study, inflationary perturbation spectra and the quantity r + 8n(T) were computed to the next-to-next-to-leading log order in quantum gravity with solely virtual particles. The spectra are functions of inflationary running coupling and satisfy cosmic renormalization group flow equations. Tensor fluctuations receive contributions from the spin-2 fakeon chi(mu nu), while the scalar spectrum's dependence on chi(mu nu) starts from alpha(2) corrections. The theoretical predictions have errors ranging from alpha(4) to alpha(3), and nontrivial issues regarding the fakeon projection at higher orders are discussed.