Beyond Discovery: How Three Inflated Hot Jupiters Around Evolved Stars Reveal the Fragile Final Phase of Giant Planet Migration

This arXiv preprint (v1, June 2026) reports three TESS-detected hot Jupiters—TOI-3664 b (P=3.30 d, R=1.22 RJ, M=0.36 MJ), TOI-4034 b (P=1.80 d, R=1.58 RJ, M=0.87 MJ), and TOI-6564 b (P=3.99 d, R=1.46 RJ, M=0.70 MJ)—orbiting stars at or near terminal-age main sequence. Follow-up radial velocities from CARMENES, CORALIE, and MINERVA-Australis yielded the masses; ages were derived via a multi-method approach combining Gaia astrometry, gyrochronology, PARSEC isochrones, and lithium depletion, producing 9.0+2.4/-2.1 Gyr, 5.7±0.5 Gyr, and 4.0±1.0 Gyr respectively despite similar evolutionary states driven by differing stellar masses (0.98–1.19 M⊙). The planets’ low densities and modest radius inflation track increasing stellar luminosity, supporting the hypothesis that hot Jupiters experience late-stage atmospheric heating before potential engulfment. However, the study’s small sample of three systems limits statistical power, and age uncertainties remain large enough to blur precise timing relative to the subgiant transition. Earlier TESS-based works (e.g., the 2023 Nature Astronomy sample of 14 inflated giants around subgiants) and the 2021 ApJ review on hot-Jupiter inflation both missed the narrow “age-ladder” window these objects occupy; together the datasets suggest that radius inflation accelerates only after ~80 % of main-sequence lifetime, a phase previously undersampled. The preprint correctly flags the systems as laboratories for late-stage tidal evolution, yet underplays the imminent risk that all three planets will be engulfed within ~100 Myr once their hosts ascend the red-giant branch—an outcome predicted by Veras et al. (2022) dynamical models but not quantified here.