ACT Constraints on Marginally Deformed Starobinsky Inflation

Abstract

We investigate the inflationary phenomenology of a marginally deformed Starobinsky model, motivated by quantum corrections to the $R^{2}$ term, in light of the latest cosmological observations. In this framework, the inflationary potential acquires a small deformation parameter, $\gamma$, which shifts predictions away from the exact Starobinsky limit. Using the slow-roll formalism, we derive analytic expressions for the spectral index $n_{s}$ and tensor-to-scalar ratio $r$ and confront them with constraints from Planck, ACT, and DESI data. Our analysis shows that nonzero values of $\gamma$ raise both $n_{s}$ and $r$, thereby alleviating the $\gtrsim 2\sigma$ tension between the Starobinsky $R^{2}$ scenario and the ACT+DESI (P-ACT-LB) measurements, which favor $n_{s} \simeq 0.9743 \pm 0.0034$. For $N \sim 60$ $e$-foldings, the model consistently reproduces the observed amplitude of primordial perturbations while predicting tensor contributions within current observational bounds. We also demonstrate that the deformation softens the otherwise severe fine-tuning of the quartic self-coupling in minimally coupled inflation. The parameter range $\gamma \sim \mathcal{O}(10^{-3})$-$\mathcal{O}(10^{-2})$ emerges as phenomenologically viable, providing a natural extension of Starobinsky inflation compatible with present data. We conclude that marginally deformed $R^{2}$ inflation remains a compelling and testable candidate for the primordial dynamics of the Universe, with future CMB and gravitational-wave observations expected to further probe its parameter space.