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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2504.01139 |
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| _version_ | 1866915333755895808 |
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| author | Grzadkowski, Bohdan Piva, Marco |
| author_facet | Grzadkowski, Bohdan Piva, Marco |
| contents | A perturbative strategy for inflation described by two-inflaton fields is developed using a mathematical analogy with the renormalization-group. Two small quantities, $α$ and $λ$, corresponding to standard slow-roll parameters are defined and systematic expansions of all inflationary quantities in terms of powers of $α$ and $λ$ are found. No other slow-roll parameters are needed. To illustrate this perturbative method in the multi-field context, we adopt a simple two-inflaton model with quadratic potentials in the parameter range where both fields contribute similarly to the dynamics of inflation. The model, even though it is not a viable alternative for phenomenological description of the inflationary period, nicely illustrates subtleties of the perturbative approach. In particular, this method allows us to derive two independent gauge-invariant scalar perturbations that are conserved in the superhorizon limit, overcoming typical problems that emerge in multi-field inflation. Furthermore, it is possible to perform nonperturbative resummations that allow to study the model in a true multi-field regime. We derive tensor and scalar power spectra to the next-to-next-to-leading and next-to-leading orders, respectively, as well as their spectral indices. The hierarchy between the two scalar perturbations allows us to single out the dominant entry of the scalar power-spectrum matrix. Modifications due to the second inflaton occur already at the leading order. Finally, we explain why the quadratic two-inflaton model is not compatible with the present experimental constraints even though non-trivial corrections to scalar perturbations do emerge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01139 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power Spectra in Double-Field Inflation Using Renormalization-Group Techniques Grzadkowski, Bohdan Piva, Marco High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology A perturbative strategy for inflation described by two-inflaton fields is developed using a mathematical analogy with the renormalization-group. Two small quantities, $α$ and $λ$, corresponding to standard slow-roll parameters are defined and systematic expansions of all inflationary quantities in terms of powers of $α$ and $λ$ are found. No other slow-roll parameters are needed. To illustrate this perturbative method in the multi-field context, we adopt a simple two-inflaton model with quadratic potentials in the parameter range where both fields contribute similarly to the dynamics of inflation. The model, even though it is not a viable alternative for phenomenological description of the inflationary period, nicely illustrates subtleties of the perturbative approach. In particular, this method allows us to derive two independent gauge-invariant scalar perturbations that are conserved in the superhorizon limit, overcoming typical problems that emerge in multi-field inflation. Furthermore, it is possible to perform nonperturbative resummations that allow to study the model in a true multi-field regime. We derive tensor and scalar power spectra to the next-to-next-to-leading and next-to-leading orders, respectively, as well as their spectral indices. The hierarchy between the two scalar perturbations allows us to single out the dominant entry of the scalar power-spectrum matrix. Modifications due to the second inflaton occur already at the leading order. Finally, we explain why the quadratic two-inflaton model is not compatible with the present experimental constraints even though non-trivial corrections to scalar perturbations do emerge. |
| title | Power Spectra in Double-Field Inflation Using Renormalization-Group Techniques |
| topic | High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2504.01139 |