Squeezed vacua and primordial features in effective theories of inflation at N2LO
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arXiv
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| Format: | Preprint |
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2024
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| author | Bianchi, Eugenio Gamonal, Mauricio |
| author_facet | Bianchi, Eugenio Gamonal, Mauricio |
| contents | A finite duration of cosmic inflation can result in features $\mathcal{P}_{\mathcal{R}}(k) = |α_k-β_k\,\mathrm{e}^{\mathrm{i}δ_k}|^2 \,\mathcal{P}_{\mathcal{R}}^{(0)}(k)$ in the primordial power spectrum that carry information about a quantum gravity phase before inflation. While the almost scale-invariant power spectrum $\mathcal{P}_{\mathcal{R}}^{(0)}$ for the quasi-Bunch-Davies vacuum is fully determined by the inflationary background dynamics, the Bogoliubov coefficients $α_k$ and $β_k$ for the squeezed vacuum depend on new physics beyond inflation and have been used to produce phenomenological templates for the features. The phase $δ_k$ vanishes in de Sitter space and therefore is often neglected, but it results in non-trivial effects in quasi-de Sitter inflationary geometries. Here we consider a large class of effective theories of inflation and provide a closed-form expression for $δ_k$ and for the fully expanded power spectrum up to next-to-next-leading order (N2LO) in the Hubble-flow expansion. In particular, for the Starobinsky model of inflation we find that this relative phase can be expressed in terms of the scalar tilt $n_\mathrm{s}$ as $δ_{k\ast}=\fracπ{2}(n_\mathrm{s}-1)-\fracπ{4}(n_\mathrm{s}-1)^2\,\ln(k/k_*)$. The relative phase results in a negative shift and a running frequency that have been considered in the most studied phenomenological templates for primordial features, thus providing precise theoretical predictions for upcoming cosmological observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Squeezed vacua and primordial features in effective theories of inflation at N2LO Bianchi, Eugenio Gamonal, Mauricio General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory A finite duration of cosmic inflation can result in features $\mathcal{P}_{\mathcal{R}}(k) = |α_k-β_k\,\mathrm{e}^{\mathrm{i}δ_k}|^2 \,\mathcal{P}_{\mathcal{R}}^{(0)}(k)$ in the primordial power spectrum that carry information about a quantum gravity phase before inflation. While the almost scale-invariant power spectrum $\mathcal{P}_{\mathcal{R}}^{(0)}$ for the quasi-Bunch-Davies vacuum is fully determined by the inflationary background dynamics, the Bogoliubov coefficients $α_k$ and $β_k$ for the squeezed vacuum depend on new physics beyond inflation and have been used to produce phenomenological templates for the features. The phase $δ_k$ vanishes in de Sitter space and therefore is often neglected, but it results in non-trivial effects in quasi-de Sitter inflationary geometries. Here we consider a large class of effective theories of inflation and provide a closed-form expression for $δ_k$ and for the fully expanded power spectrum up to next-to-next-leading order (N2LO) in the Hubble-flow expansion. In particular, for the Starobinsky model of inflation we find that this relative phase can be expressed in terms of the scalar tilt $n_\mathrm{s}$ as $δ_{k\ast}=\fracπ{2}(n_\mathrm{s}-1)-\fracπ{4}(n_\mathrm{s}-1)^2\,\ln(k/k_*)$. The relative phase results in a negative shift and a running frequency that have been considered in the most studied phenomenological templates for primordial features, thus providing precise theoretical predictions for upcoming cosmological observations. |
| title | Squeezed vacua and primordial features in effective theories of inflation at N2LO |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.11812 |