Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections
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| Format: | Preprint |
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2025
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| _version_ | 1866908685646692352 |
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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 |
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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 |