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

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 ($m_{\chi }>m_{\varphi }/4$) on the mass $m_{\chi }$ of the fakeon with respect to the mass $m_{\varphi }$ 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.

39 pages, 1 figure; v2: minor changes, JHEP

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