Beyond the Starobinsky model after ACT

Abstract

We revisit higher order corrections to the Starobinsky inflationary model using the most recent P-ACT-LB-BK18 data, which exhibits a mild but definite tension with the predictions of the original model. Our results demonstrate how even small {higher order} deformations of the Ricci scalar (e.g. $R^3, R^4,\cdots$) can bring the model into better agreement with current data and impose nontrivial constraints on the post-inflationary dynamics.

Figures (5)

• Figure 1: The Einstein–frame potential $V_E(s)$. The black solid line represents the original Starobinsky model ($\delta = 0$), while the colored dashed lines correspond to the $R^3$ term included potential as in Eq. \ref{['eq:Einstein_V_exact']}.
• Figure 2: $(n_s, r)$ plane with varying $N_e$ and $\delta$ (in units of $10^{-4}$), under the assumption of matter-dominated reheating ($w_{\rm eff} = 0$). The shaded regions show the $1\sigma$ and $2\sigma$ constraints from P-ACT-LB-BK18 (yellow and green), while the dashed lines denote the $1\sigma$ (blue) and $2\sigma$ (red) bounds from Planck 2018. The colored solid lines correspond to $N_e=42, 45, 50, 55$, with the color bar indicating the associated reheating temperature $T_{\mathrm {re}}$ and $N_e$. The black dashed line shows the trajectory for $N_e = 60$, which is not included in the color bar.
• Figure 3: Allowed region in the $(\delta, T)$ plane (with $\delta$ in units of $10^{-4}$) under the assumption of matter-dominated reheating ($w_{\rm eff} = 0$). The shaded regions represent the $1\sigma$ (yellow) and $2\sigma$ (green) constraints from P-ACT-LB-BK18, while the dashed lines denote the $1\sigma$ (blue) and $2\sigma$ (red) bounds from Planck 2018. The horizontal black line indicates the benchmark point corresponding to the perturbative decay scenario with $N_e \simeq 50.6$ and $T_{\mathrm{re}} \simeq 5.1\times10^{9}\,\mathrm{GeV}$.
• Figure 4: Predictions in the $(n_s, T)$ plane for varying $\delta$ and $w_{\rm eff}$. Each group of five lines corresponds to a fixed value of $\delta$ (in units of $10^{-4}$). Within each group, the lines represent different values of the equation-of-state parameter $w_{\rm eff} = -1/3$ (red), $0$ (orange), $1/5$ (yellow), $1/3$ (green), $3/5$ (blue) and $1$ (purple). The shaded regions correspond to the $1\sigma$ (yellow) and $2\sigma$ (green) bounds on $n_s$ from P-ACT-LB-BK18.
• Figure 5: Allowed region in the $(\delta, w_{\rm eff})$ plane, showing the combinations of $\delta$ (in units of $10^{-4}$) and the effective equation-of-state parameter $w_{\rm eff}$ that are consistent with observations. The shaded regions correspond to the $1\sigma$ (yellow) and $2\sigma$ (green) constraints from P-ACT-LB-BK18.