Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term. (English) Zbl 1451.83112
Summary: 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 \((4/2 < N^2r <12\) 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 degrees of freedom are present.
MSC:
| 83F05 | Relativistic cosmology |
| 85A40 | Astrophysical cosmology |
| 83C45 | Quantization of the gravitational field |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
| 53Z05 | Applications of differential geometry to physics |
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