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

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Main Authors: Bianchi, Eugenio, Gamonal, Mauricio
Format: Preprint
Published: 2025
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author Bianchi, Eugenio
Gamonal, Mauricio
author_facet Bianchi, Eugenio
Gamonal, Mauricio
contents Starobinsky's $R+αR^2$ 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 $R+αR^2 - βW^2$, 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 $c_{\textrm{s}}$ for scalar and $c_{\textrm{t}}$ for tensor modes, satisfying the relation $c_{\textrm{t}}/c_{\textrm{s}} \simeq 1+ \fracβ{6\, α}$ 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 $r \simeq 3(1-\fracβ{6α})(n_\textrm{s}-1)^2$, the tensor tilt $n_{\textrm{t}}\simeq-\frac{r}{8}$ and the running of the scalar tilt $\mathfrak{a}_{\textrm{s}}\simeq-\frac{1}{2} (n_{\textrm{s}} - 1)^2$, all expressed in terms of the observed scalar tilt $n_{\textrm{s}}$. We also provide the corresponding corrections up to N3LO, $\mathcal{O}((n_{\textrm{s}} - 1)^3)$.
format Preprint
id arxiv_https___arxiv_org_abs_2506_10081
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections
Bianchi, Eugenio
Gamonal, Mauricio
General Relativity and Quantum Cosmology
Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
Starobinsky's $R+αR^2$ 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 $R+αR^2 - βW^2$, 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 $c_{\textrm{s}}$ for scalar and $c_{\textrm{t}}$ for tensor modes, satisfying the relation $c_{\textrm{t}}/c_{\textrm{s}} \simeq 1+ \fracβ{6\, α}$ 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 $r \simeq 3(1-\fracβ{6α})(n_\textrm{s}-1)^2$, the tensor tilt $n_{\textrm{t}}\simeq-\frac{r}{8}$ and the running of the scalar tilt $\mathfrak{a}_{\textrm{s}}\simeq-\frac{1}{2} (n_{\textrm{s}} - 1)^2$, all expressed in terms of the observed scalar tilt $n_{\textrm{s}}$. We also provide the corresponding corrections up to N3LO, $\mathcal{O}((n_{\textrm{s}} - 1)^3)$.
title Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections
topic General Relativity and Quantum Cosmology
Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
url https://arxiv.org/abs/2506.10081