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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.15991 |
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| _version_ | 1866912911219228672 |
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| author | Oliveira, Daniel Rasouli, Seyed Marto, Joao Moniz, Paulo |
| author_facet | Oliveira, Daniel Rasouli, Seyed Marto, Joao Moniz, Paulo |
| contents | Power-law inflation with $a(t) \propto t^m$ is conceptually simple and predicts a scalar tilt $n_s = 1 - 2/m$ compatible with CMB data, but in four-dimensional Einstein gravity it typically yields a tensor-to-scalar ratio $r = 16/m$ that is too large to satisfy current bounds. We show that a minimal extension based on fractional scalar-field cosmology resolves this tension. Introducing a fractional order $α\neq 1$ generates non-local (memory) corrections in the Friedmann and Klein-Gordon dynamics that suppress $r$ while keeping $n_s$ essentially unchanged. We derive an explicit mapping $α(n,m)$ and recover the standard power-law limit as $α\to 1$. For observationally favored values $α\approx 0.8$-$0.9$ in four dimensions we obtain $n_s \approx 0.965$ and $r \lesssim 0.04$, bringing power-law inflation into agreement with data. The scalar potential follows self-consistently as an exponential, and a dynamical-systems analysis shows the fractional power-law solutions form stable inflationary attractors over the viable parameter range. These results establish fractional power-law inflation as a predictive and testable framework, with clear targets for forthcoming CMB polarization measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15991 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Power-Law Inflation in n-Dimensional Fractional Scalar Field Cosmology: Observational Constraints and Dynamical Analysis Oliveira, Daniel Rasouli, Seyed Marto, Joao Moniz, Paulo General Relativity and Quantum Cosmology Power-law inflation with $a(t) \propto t^m$ is conceptually simple and predicts a scalar tilt $n_s = 1 - 2/m$ compatible with CMB data, but in four-dimensional Einstein gravity it typically yields a tensor-to-scalar ratio $r = 16/m$ that is too large to satisfy current bounds. We show that a minimal extension based on fractional scalar-field cosmology resolves this tension. Introducing a fractional order $α\neq 1$ generates non-local (memory) corrections in the Friedmann and Klein-Gordon dynamics that suppress $r$ while keeping $n_s$ essentially unchanged. We derive an explicit mapping $α(n,m)$ and recover the standard power-law limit as $α\to 1$. For observationally favored values $α\approx 0.8$-$0.9$ in four dimensions we obtain $n_s \approx 0.965$ and $r \lesssim 0.04$, bringing power-law inflation into agreement with data. The scalar potential follows self-consistently as an exponential, and a dynamical-systems analysis shows the fractional power-law solutions form stable inflationary attractors over the viable parameter range. These results establish fractional power-law inflation as a predictive and testable framework, with clear targets for forthcoming CMB polarization measurements. |
| title | Power-Law Inflation in n-Dimensional Fractional Scalar Field Cosmology: Observational Constraints and Dynamical Analysis |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2602.15991 |