Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term

TL;DR

This paper predicts inflationary cosmology observables using quantum gravity with fakeons, focusing on the effects of the Weyl-squared term, and establishes bounds on fakeon mass and tensor-to-scalar ratio.

Contribution

It introduces a novel quantum gravity approach with fakeons in inflationary models, analyzing the impact of the Weyl-squared term on spectral indices and tensor-to-scalar ratio.

Findings

Tensor-to-scalar ratio predicted within less than an order of magnitude

The relation r ≈ -8n_T remains unaffected by the Weyl-squared term

Lower bound on fakeon mass m_χ > m_φ/4

Abstract

We derive the predictions of quantum gravity with fakeons on the amplitudes and spectral indices of the scalar and tensor fluctuations in inflationary cosmology. The action is $R+R^{2}$ plus the Weyl-squared term. The ghost is eliminated by turning it into a fakeon, that is to say a purely virtual particle. We work to the next-to-leading order of the expansion around the de Sitter background. The consistency of the approach puts a lower bound ($ m_{\chi }>m_{\phi }/4$) on the mass $m_{\chi }$ of the fakeon with respect to the mass $m_{\phi }$ of the inflaton. The tensor-to-scalar ratio $r$ is predicted within less than an order of magnitude ($4/3<N^{2}r<12$ to the leading order in the number of $e$-foldings $N$). Moreover, the relation $r\simeq -8n_{T}$ is not affected by the Weyl-squared term. No vector and no other scalar/tensor degree of freedom is present.