Since the discovery of the first transiting hot Jupiters, models have sought to explain the anomalously large radii of highly irradiated gas giants. We now know that the size of hot Jupiter radius anomalies scales strongly with a planet's level of irradiation and numerous models like tidal heating, ohmic dissipation, and thermal tides have since been developed to help explain these inflated radii. In general, however, these models can be grouped into two broad categories: models that directly inflate planetary radii by depositing a fraction of the incident irradiation into the interior and models that simply slow a planet's radiative cooling, allowing it to retain more heat from formation and thereby delay contraction. Here we present a new test to distinguish between these two classes of models. Gas giants orbiting at moderate orbital periods around post-main-sequence stars will experience enormous increases to their irradiation as their host stars move up the sub-giant and red-giant branches. If hot Jupiter inflation works by depositing irradiation into the planet's deep interiors then planetary radii should increase in response to the increased irradiation. This means that otherwise non-inflated gas giants at moderate orbital periods of 10 days can re-inflate as their host stars evolve. Here we explore the circumstances that can lead to the creation of these "re-inflated" gas giants and examine how the existence or absence of such planets can be used to place unique constraints on the physics of the hot Jupiter inflation mechanism. Finally, we explore the prospects for detecting this potentially important undiscovered population of planets.
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