Inflationary dynamics in modified gravity models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909173877309440 |
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| author | Cuzinatto, R. R. Medeiros, L. G. |
| author_facet | Cuzinatto, R. R. Medeiros, L. G. |
| contents | Higher-order theories of gravity are a branch of modified gravity wherein the geometrodynamics of the four-dimensional Riemannian manifold is determined by field equations involving derivatives of the metric tensor of order higher than two. This paper considers a general action built with the Einstein-Hilbert term plus additional curvature-based invariants, viz. the Starobinsky $R^{2}$-type term, a term scaling with $R^{3}$, and a correction of the type $R\square R$. The focus is on the background inflationary regime accommodated by these three models. For that, the higher-order field equations are built and specified for the FLRW line element. The dynanical analysis in the phase space is carried in each case. This analysis shows that the Starobinsky-plus-$R^{3}$ model keeps the good features exhibited by the pure Starobinsky inflationary model, although the set of initial conditions for the inflaton field $χ$ leading to a graceful exit scenario is more contrived; the coupling constant $α_{0}$ of the $R^{3}$ invariant is also constrained by the dynamical analysis. The Starobinsky-plus-$R\square R$ model turns out being a double-field inflation model; it consistently enables an almost-exponential primordial acceleration followed by a radiation dominated universe if its coupling $β_{0}$ takes values in the interval $0\leqβ_{0}\leq3/4$. The models introducing higher-order correction to Starobinsky inflation are interesting due to the possibility of a running spectral index $n_{s}$, something that is allowed by current CMB observations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_11904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inflationary dynamics in modified gravity models Cuzinatto, R. R. Medeiros, L. G. General Relativity and Quantum Cosmology Higher-order theories of gravity are a branch of modified gravity wherein the geometrodynamics of the four-dimensional Riemannian manifold is determined by field equations involving derivatives of the metric tensor of order higher than two. This paper considers a general action built with the Einstein-Hilbert term plus additional curvature-based invariants, viz. the Starobinsky $R^{2}$-type term, a term scaling with $R^{3}$, and a correction of the type $R\square R$. The focus is on the background inflationary regime accommodated by these three models. For that, the higher-order field equations are built and specified for the FLRW line element. The dynanical analysis in the phase space is carried in each case. This analysis shows that the Starobinsky-plus-$R^{3}$ model keeps the good features exhibited by the pure Starobinsky inflationary model, although the set of initial conditions for the inflaton field $χ$ leading to a graceful exit scenario is more contrived; the coupling constant $α_{0}$ of the $R^{3}$ invariant is also constrained by the dynamical analysis. The Starobinsky-plus-$R\square R$ model turns out being a double-field inflation model; it consistently enables an almost-exponential primordial acceleration followed by a radiation dominated universe if its coupling $β_{0}$ takes values in the interval $0\leqβ_{0}\leq3/4$. The models introducing higher-order correction to Starobinsky inflation are interesting due to the possibility of a running spectral index $n_{s}$, something that is allowed by current CMB observations. |
| title | Inflationary dynamics in modified gravity models |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2404.11904 |