Globally stable, ghost-free hyperbolic square-root deformation of the Starobinsky model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912959520833536 |
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| author | Galiautdinov, Andrei |
| author_facet | Galiautdinov, Andrei |
| contents | We propose an exact, analytic deformation of the Starobinsky model governed by the strictly positive derivative of its Lagrangian, $f'(R) = αR + \sqrt{α^2 R^2 + 1}$, with $α> 0$. This geometric hyperbolic square-root ansatz is designed to eliminate the well-known strong-coupling singularity that arises in quadratic $f(R)$ gravity when $f'(R)=0$. The construction seamlessly recovers general relativity at low curvatures and preserves the successful slow-roll inflationary plateau at extreme positive curvatures. In the limit $R \to -\infty$, the derivative $f'(R)$ asymptotes to zero strictly from above, removing the pathological branch associated with the vanishing of $f'(R)$. This guarantees that the only admissible constant-curvature ($R=A$) solutions correspond to standard Einstein spaces with an effective cosmological constant $Λ_{\text{eff}} \equiv A/4$. The first and second derivatives of the action, as well as the scalaron mass squared, remain strictly positive globally, ensuring a perfectly ghost-free and tachyon-free cosmological evolution across the entire spacetime manifold. In the Einstein frame, the dynamics of the scalaron is governed by the globally defined potential $V(ϕ) = \frac{1}{8α} [ 1 - (1 + 2\sqrt{2/3}ϕ) \exp(-2\sqrt{2/3}ϕ) ] + Λ\exp(-2\sqrt{2/3}ϕ)$, which naturally establishes an impenetrable energetic wall as $ϕ\to -\infty$, offering a robust, globally stable mechanism for non-singular bouncing cosmologies. For $N = 60$ inflationary e-folds, the model predicts a scalar spectral index of $n_s \simeq 0.967$ and a strongly suppressed tensor-to-scalar ratio of $r \simeq 0.00083$, which position the proposed theory within the observationally favored parameter space of the Planck and BICEP/Keck Array baseline constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09944 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Globally stable, ghost-free hyperbolic square-root deformation of the Starobinsky model Galiautdinov, Andrei General Relativity and Quantum Cosmology We propose an exact, analytic deformation of the Starobinsky model governed by the strictly positive derivative of its Lagrangian, $f'(R) = αR + \sqrt{α^2 R^2 + 1}$, with $α> 0$. This geometric hyperbolic square-root ansatz is designed to eliminate the well-known strong-coupling singularity that arises in quadratic $f(R)$ gravity when $f'(R)=0$. The construction seamlessly recovers general relativity at low curvatures and preserves the successful slow-roll inflationary plateau at extreme positive curvatures. In the limit $R \to -\infty$, the derivative $f'(R)$ asymptotes to zero strictly from above, removing the pathological branch associated with the vanishing of $f'(R)$. This guarantees that the only admissible constant-curvature ($R=A$) solutions correspond to standard Einstein spaces with an effective cosmological constant $Λ_{\text{eff}} \equiv A/4$. The first and second derivatives of the action, as well as the scalaron mass squared, remain strictly positive globally, ensuring a perfectly ghost-free and tachyon-free cosmological evolution across the entire spacetime manifold. In the Einstein frame, the dynamics of the scalaron is governed by the globally defined potential $V(ϕ) = \frac{1}{8α} [ 1 - (1 + 2\sqrt{2/3}ϕ) \exp(-2\sqrt{2/3}ϕ) ] + Λ\exp(-2\sqrt{2/3}ϕ)$, which naturally establishes an impenetrable energetic wall as $ϕ\to -\infty$, offering a robust, globally stable mechanism for non-singular bouncing cosmologies. For $N = 60$ inflationary e-folds, the model predicts a scalar spectral index of $n_s \simeq 0.967$ and a strongly suppressed tensor-to-scalar ratio of $r \simeq 0.00083$, which position the proposed theory within the observationally favored parameter space of the Planck and BICEP/Keck Array baseline constraints. |
| title | Globally stable, ghost-free hyperbolic square-root deformation of the Starobinsky model |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.09944 |