  We explore the minimum distance from a host star where an exoplanet could
potentially be habitable in order not to discard close-in rocky exoplanets for
follow-up observations. We find that the inner edge of the Habitable Zone for
hot desert worlds can be as close as 0.38 AU around a solar-like star, if the
greenhouse effect is reduced ($\sim$ 1% relative humidity) and the surface
albedo is increased. We consider a wide range of atmospheric and planetary
parameters such as the mixing ratios of greenhouse gases (water vapor and
CO$_2$), surface albedo, pressure and gravity. Intermediate surface pressure
($\sim$1-10 bars) is necessary to limit water loss and to simultaneously
sustain an active water cycle. We additionally find that the water loss
timescale is influenced by the atmospheric CO$_2$ level, because it indirectly
influences the stratospheric water mixing ratio. If the CO$_2$ mixing ratio of
dry planets at the inner edge is smaller than 10$^{-4}$, the water loss
timescale is $\sim$1 billion years, which is considered here too short for life
to evolve. We also show that the expected transmission spectra of hot desert
worlds are similar to an Earth-like planet. Therefore, an instrument designed
to identify biosignature gases in an Earth-like atmosphere can also identify
similarly abundant gases in the atmospheres of dry planets. Our inner edge
limit is closer to the host star than previous estimates. As a consequence, the
occurrence rate of potentially habitable planets is larger than previously
thought.
