High-order corrections to inflationary perturbation spectra in quantum gravity

Abstract

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 $\alpha (1/k)$ 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 ${\chi }_{\mu \nu }$ at every order of the expansion in powers of $\alpha \sim 1/115$. The dependence of the scalar spectrum on the ${\chi }_{\mu \nu }$ mass $m_{\chi }$, on the other hand, starts from the ${\alpha }^2$ corrections, which are handled perturbatively in the ratio $m_{\varphi }/m_{\chi }$, where $m_{\varphi }$ is the inflaton mass. The predictions have theoretical errors ranging from ${\alpha }^4\sim 10^{-8}$ to ${\alpha }^3\sim 10^{-6}$. Nontrivial issues concerning the fakeon projection at higher orders are addressed.

28 pages; JCAP

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• Entropy Production in the Inflationary Epoch Using the Gouy-Stodola Theorem
• Purely Virtual Particles in Quantum Gravity, Inflationary Cosmology and Collider Physics
• Quantum gravity with purely virtual particles from asymptotically local quantum field theory
• Cosmological inhomogeneities, primordial black holes, and a hypothesis on the death of the universe