Preventing Curvature Singularities in $f(R)$ Dark Energy Models

Abstract

The curvature singularity problem in $f(R)$ dark energy models poses a significant challenge to their viability as alternatives to the $\Lambda$CDM paradigm. In this work, we investigate the possibility of resolving this issue by incorporating higher-order corrections that are compatible with the inflationary phase. We analyze the effects of adding $R^2$, $R^{\frac{m+2}{m+1}}$ and $\alpha$-attractor representation in $f(R)$ gravity terms to types of dark energy $f(R)$ models, focusing on their ability to prevent singularities in high-density environments. Our results demonstrate that these corrections can effectively stabilize the models, ensuring their consistency across both inflationary and late-time cosmological scales.

25 pages, 8 figures

References in corpus (17)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Are f(R) dark energy models cosmologically viable ?
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• The Unity of Cosmological Attractors
• The (pseudo)issue of the conformal frame revisited
• Planck, LHC, and $\alpha$-attractors
• Time-dependent matter instability and star singularity in $F(R)$ gravity
• Consistency relation for $R^p$ inflation
• Towards Axionic Starobinsky-like Inflation in String Theory
• Reheating in Constant-roll $F(R)$ Gravity
• Reconstructing a $f(R)$ theory from the $\alpha$-Attractors
• Disentangling the $f(R)$ - Duality
• Matter Power Spectra in Viable $f(R)$ Gravity Models with Dynamical Background
• Inflationary $\alpha -$attractors and $F(R)$ gravity