The standard solar model predicts a young Sun which was too faint to sustain liquid water on the Earth, unless there was an extreme greenhouse effect at the time, which seems to contradict the geochemical record. It seems to be almost impossible to get liquid water on Mars under the standard solar model with any plausible early Mars atmosphere.
Here is an interesting article on an old problem…
Astrobiology Magazine picked this up through the actual reporter finding it out by reading proposal abstracts. Which is impressive but scare:
The basic idea is to look at solar models in which the young Sun was a little bit more massive, and got to its current mass through an enhanced stellar wind over the first few hundred million years.
This is an old idea, well explored by Sackmann and Boothroyd (2003), but for various reasons it may be timely to look at it again in detail.