Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections

Eugenio Bianchi; Mauricio Gamonal

doi:10.1103/vyls-33np

paper

Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections

arXiv:2506.10081 · doi:10.1103/vyls-33np

Abstract

Starobinsky's $R + α R^{2}$ inflation provides a compelling one-parameter inflationary model that is supported by current cosmological observations. However, at the same order in spacetime derivatives as the $R^{2}$ term, an effective theory of spacetime geometry must also include the Weyl-squared curvature invariant $W^{2}$ . In this paper, we study the inflationary predictions of the gravitational theory with action of the form $R + α R^{2} - β W^{2}$ , where the coupling constant $α$ sets the scale of inflation, and corrections due to the $W^{2}$ term are treated self-consistently via reduction of order in an expansion in the coupling constant $β$ , at the linear order in $β / α$ . Cosmological perturbations are found to be described by an effective action with a nontrivial speed of sound $c_{s}$ for scalar and $c_{t}$ for tensor modes, satisfying the relation $c_{t} / c_{s} ≃ 1 + \frac{β}{6 α}$ during the inflationary phase. Within this self-consistent framework, we compute several primordial observables up to the next-to-next-to-next-to leading order (N3LO). We find the tensor-to-scalar ratio $r ≃ 3 (1 - \frac{β}{6 α}) (n_{s} - 1)^{2}$ , the tensor tilt $n_{t} ≃ - \frac{r}{8}$ and the running of the scalar tilt $a_{s} ≃ - \frac{1}{2} (n_{s} - 1)^{2}$ , all expressed in terms of the observed scalar tilt $n_{s}$ . We also provide the corresponding corrections up to N3LO, $O ((n_{s} - 1)^{3})$ .

22 pages, 3 figures, 2 tables; References added, matches published version

Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections

Abstract

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