Sun-like stars become brighter over the course of their long lives, which means that the Sun once provided Earth with far less heat than it does now - so much less, in fact, that life should have been impossible.
This is known as the faint young Sun paradox, and it was first identified by astronomers Carl Sagan and George Mullen back in 1972. In the early days of the solar system, the Sun should only have been at only about 70% its current luminosity. Such a relatively paltry amount of heat would have made it impossible for the Earth to maintain a liquid ocean, and yet we know for a fact that it did — and now that we're pretty much certain Mars had a liquid ocean back then as well, we can add that as a second mystery to the list.
The most common way to account for this apparent paradox is that the Earth simply held onto a lot more heat back then, most likely due to a runaway greenhouse effect. The absence of bacteria would have meant there was nothing around to break down carbon dioxide into its constituent parts, which would have helped fuel this greenhouse effect.
The problem, as Astrobiology Magazine reports, is that the geological record doesn't really support the carbon dioxide hypothesis. If there really was a ton of this gas in the early atmosphere, then minerals like siderite — which forms in the presence of heavy concentrations of carbon dioxide — should be everywhere in the ancient geological record. But it's almost completely absent, which makes it hard to credit this particular hypothesis.
It gets worse. Even if we can sort out the Earth side of the equation, we now have Mars to worry about as well, which makes the problem more complicated now than it had been in previous decades. Since Mars is much further out, you would need a lot more carbon dioxide to create the greenhouse gas effect — so much, in fact, that the carbon dioxide would blot out the Sun and start reflecting the Sun's rays, not trapping them. It's like we've traded one paradox for another.
That's where an alternative hypothesis enters the picture. A Penn State research team led by Stein Sigurdsson has created a new computer model that can simulate the Sun's evolution under various different starting condition. What they're searching for is the right combination of starting elements and internal conditions that could support an old, largely disregarded explanation: that the Sun was once more massive than it is now, and a fierce solar wind shrunk it to its present size.
The exact estimates vary on how big the Sun must once have been — the range is somewhere between 2% and 10% larger — but the idea is that the additional mass made the ancient Sun compensated for its relatively inefficient release of sunlight. This means its luminosity was effectively the same then as it is now, only for different reasons. This removes the need for any greenhouse effect and explains why we can't find evidence of one in the geological record.
Of course, the paradox isn't going away that easily. The solar wind must once have been at least a thousand times more powerful than it is now. Evidence from meteorites suggests that there once was an increased solar wind, but it could only have lasted for about 100 million years. In cosmic terms, that's barely any time at all for the Sun to blow off a significant chunk of its mass and slim down to its current size.
The other concern is that we simply haven't observed any other Sun-like stars behaving like this. All other medium-sized stars start out their life far less luminous, then slowly warm up over billions of years - indeed, without that observational data to guide our modeling of stellar evolution, there wouldn't have been any paradox to worry about in the first place. This hypothesis comes perilously close to carving out a unique path for our Sun's evolution, and scientists are leery of relying on explanations that require extraordinary circumstances in order to work.
However this paradox is resolved, it seems it is not going away quietly. About the only thing we can be sure of is that, somehow, the Earth and its oceans did survive. I think we can take that much for granted... unless this is the mother of all Twilight Zone twists and we all suddenly realize Earth was frozen the whole time. I don't really think that can be considered a hypothesis though...