  Earth's earliest sedimentary record contains evidence that surface
temperatures were similar to, or perhaps even warmer than modern. In contrast,
standard Solar models suggest the Sun was 25% less luminous at this ancient
epoch, implying a cold, frozen planet-all else kept equal. This discrepancy,
known as the Faint Young Sun Paradox, remains unresolved. Most proposed
solutions invoke high concentrations of greenhouse gases in the early
atmosphere to offset for the fainter Sun, though current geological constraints
are insufficient to verify or falsify these scenarios. In this work, we
examined several simple mechanisms that involve the role played by Earth's spin
rate, which was significantly faster during Archean time. This faster spin rate
enhances the equator-to-pole temperature gradient, facilitating a warm equator,
while maintaining cold poles. Results show that such an enhanced meridional
gradient augments the meridional gradient in carbonate deposition, which biases
the surviving geological record away from the global mean, toward warmer
waters. Moreover, using simple atmospheric models, we found that the
faster-spinning Earth was less sensitive to ice-albedo feedbacks, facilitating
larger meridional temperature gradients before succumbing to global glaciation.
We show that within the faster-spinning regime, the greenhouse warming required
to generate an ice-free Earth can differ from that required to generate an
Earth with permanent ice caps by the equivalent of 1-2 orders of magnitude of
pCO2. Accordingly, the resolution of the Faint Young Sun problem depends
significantly on whether the early Earth was ever, or even at times, ice-free.
