Starobinsky Inflation in k-Essence Framework: Attractor Dynamics, Reheating, and Consistency with ACT DR6

Abstract

The recent ACT DR6 has shifted the preferred value of the scalar spectral index upward so that many well-established inflationary models have been disfavoured, including the Starobinsky potential. Despite this, the Starobinsky potential remains exceptionally well-motivated, with origins in $R^2$ gravity, no-scale supergravity, and the $α$-attractor framework. In this work, we show that the Starobinsky potential can be fully revived within a k-essence framework, described by the Lagrangian $\mathcal{L} = F(ϕ)X - V(ϕ)$, with a power-law kinetic coupling $F(ϕ) = 1+Aϕ^n$ and no modification to the gravitational sector. Solving the background equations numerically, we find that the predictions for $n_s$, $α_s$, and $r$ fall within the $1σ$ region of ACT DR6 for a well-defined range of the coupling parameters. The attractor behavior of the inflationary solution is confirmed both analytically through the Hamilton-Jacobi formalism and numerically via a phase-space analysis. For the reheating phase, it is discussed that due to the nature of the Starobinsky potential, the effective equation of state parameter is fixed as $w_{\rm re} = 0$, resulting in a reheating temperature $T_{\rm re} \sim 10^{14}~{\rm GeV}$, well above the BBN bound. The relic gravitational wave spectrum is also computed and it is found that they can lie within the sensitivity bound of the BBO. These results demonstrate that the Starobinsky potential remains a theoretically viable candidate for inflation and that its incompatibility with ACT DR6 in the canonical setting can be resolved by introducing a simple non-canonical kinetic coupling without any modification to the underlying gravitational theory.