A Starobinsky-like Potential 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 R2 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 ℒ = F(ϕ)X − V(ϕ), with a power-law kinetic coupling F(ϕ) = 1+Aϕn and no modification to the gravitational sector. Solving the background equations numerically, we find that the predictions for ns, αs, 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 wre = 0, resulting in a reheating temperature Tre ∼ 1014 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.
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BibTeX
@misc{mohammadi2026starobinskylike,
title = {{A Starobinsky-like Potential in k-Essence Framework: Attractor Dynamics, Reheating, and Consistency with ACT DR6}},
author = {Abolhassan Mohammadi and Yogesh and Hongwei Tan and M. Sami},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.06112},
eprint = {2607.06112},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.06112},
}
RIS
TY - UNPB
TI - A Starobinsky-like Potential in k-Essence Framework: Attractor Dynamics, Reheating, and Consistency with ACT DR6
AU - Abolhassan Mohammadi
AU - Yogesh
AU - Hongwei Tan
AU - M. Sami
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2607.06112
UR - https://arxiv.org/abs/2607.06112
AB - 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 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_re = 0, resulting in a reheating temperature T_re ∼ 10^14 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.
ER -