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

The curvature singularity problem in $f(R)$ dark energy models poses a significant challenge to their viability as alternatives to the $\mathrm{\Lambda }$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.