  Young terrestrial planets can capture or outgas hydrogen-rich atmospheres
with tens to hundreds of bars of H2, which persist for 100 Myrs or longer.
Although the earliest habitable conditions on Earth and terrestrial exoplanets
could thus arise while the atmosphere is still dominated by H2, the climatic
effects of H2 remain poorly understood. Previous work showed that H2 induces
strong greenhouse warming at the outer edge of the habitable zone. Here we use
a 1D radiative-convective model to show that H2 also leads to strong warming
near the inner edge of the habitable zone. Unlike H2's greenhouse warming at
the outer edge, however, its effect near the inner edge is driven by
thermodynamics: H2's large thermal scale height allows the atmosphere to store
more water vapor than either a pure-H2O atmosphere or an atmosphere with a
heavy background gas, such as N2 or CO2, thereby amplifying the greenhouse
effect of H2O. Using idealized grey calculations, we then present a general
argument for how different background gases affect the inner edge of the
habitable zone. H2 stands out for its ability to induce novel "Souffle"
climates, which further support its warming effect. Our results show that if
the earliest conditions on a planet near the inner edge of the habitable zone
were H2-rich, they were likely also hot: 1 bar of H2 is sufficient to raise
surface temperatures above 340 K, and 50 bar of H2 are sufficient to raise
surface temperatures above 450 K.
