
I noticed that the $\ce{CO2}$ is actually decreasing in the eon time.
My guess is lush vegetation or forests began to grow which absorbed the $\ce{CO2}$ by photosynthesis? Would anyone give me any clue?

I noticed that the $\ce{CO2}$ is actually decreasing in the eon time.
My guess is lush vegetation or forests began to grow which absorbed the $\ce{CO2}$ by photosynthesis? Would anyone give me any clue?
The short answer is that most of the Earth's original allotment of CO2 got locked up in various carbonate minerals, largely calcite (limestone, marble, and chalk). According to this article there is currently ~800 gigatons of carbon in the atmosphere today; there is ~39,000,000 gigatons of carbon locked up in calcite minerals. All that carbon was once in the atmosphere as CO2. Rainfall dissolved CO2 into H2CO3 (carbonic acid) which then reacted with calcium-containing minerals and then precipitated out in the world's oceans where they formed early calcite deposits.
If not for this process the Earth's climate would not be too unlike Venus'.
No, it is not due to lush vegetation (that was not around until just hundreds of millions of years ago). The period around 2.5 billion years ago is known as the Great Oxygenation period. No one knows for sure, but it was probably caused by anaerobic bacteria producing oxygen for the previous billion years. They basically destroyed their environment by oxygenating Earth. We have copious quantities of iron-ore formations (the banded iron formations) around this time to prove that the earth basically rusted. The free iron in the oceans picked up oxygen and precipitated out Fe2O3. Finally oxygen got high enough about 700,000 years ago to allow the first multicellular life to evolve.
BTW I think the diagram is pure speculation but would also like to know more about the source
Also less volcanism from the crust thickening due to the Earth cooling and the land becoming available to photosynthesizers when the oxygen caused the ozone layer. Heat would cause more $\ce{CO2}$ in the air than today which makes it hotter still until Earth's heat radiation gets strong enough. It was hot at first from all the lava and the volcanic $\ce{CO2}$ overpowering the weaker sun. When it got cooler however, temperatures caused more $\ce{CO2}$ to be incorporated into carbonate rocks and plowed back into the mantle when their plates subducted. There's still chalk on the ground from when dinosaurs roamed a warmer Earth but a lot of that huge $\ce{CO2}$ atmosphere is in the mantle thanks to plate tectonics.
There's a number of things to consider, and, I'm just a layman who's read up on this a little as a hobby.
1) Solar wind and magnetic field.
We've all heard about Mars losing it's atmosphere to the Solar wind. Young earth may have lost some of it's early atmosphere to the solar wind too - certainly some of the H2 in the chart in the original question. He as well.
Earth's magnetic field formed some 3.5 billion years ago. The earth had to cool down enough for the inner core to become solid for the magnetic field to form. Also, that first 1.1 billion years of the solar system, the sun probobly had more frequent and stronger solar wind.
Source: http://www.wired.com/2010/03/earths-magnetic-field-is-35-billion-years-old/
So for the first 1.1 billion years, the Solar wind was probobly the primary factor in affecting the earth's atmosphere. Also, if we begin the study around the time of the formation of the moon, the late heavy bombardment likely also brought frozen gas to the earth. The young solar system was a chaotic place.
Following the formation of the magnetic field and the end of the late heavy bombardment (some of those asteroids may have vaporized the entirety of the earth's oceans for a time), then life became the driving factor in atmospheric changes.
Oxygen is the one we care about, but it wasn't the first. Early forms of photosynthesis probobly included sulfur and likely all of it took place in the oceans. There's not much dissolved gas in the oceans but there's enough that over hundreds of millions of years, this would have an effect. Needless to say, once Oxygen photosynthesis started, that had a bigger effect.
Oxygen photosynthesis may have started around 2.7 billion years ago and that was huge in taking and using CO2 dissolved in the ocean (but ultimately from the atmosphere) and releasing O2.
Source: http://www.scientificamerican.com/article/timeline-of-photosynthesis-on-earth/
Initially the released O2 bonded with Iron dissolved in the oceans and later, when released into the atmosphere (about 2.3-2.4 billion years ago), it likely reacted with and removed any remaining CH4 (Methane) in earth's atmosphere and perhaps any NH3 (Ammonia). The dissolved O2 helped make the oceans clear but it also posed a problem for primitive bacteria that found dissolved oxygen far to reactive and this led to further evolution, life protecting itself from oxygen, and in time, this also lead to the ozone layer which helped early life move to the land. Oxygen was also useful in forming granite, which was lighter than Basalt and this created more permanent and higher continents.
But to your question, what's important is that some bacteria died and fell to the ocean floor and this is where most of the early CO2 went, it formed layers on the ocean floor that over time became rock.
When the first forests came, about 400 million years ago, they also played a role in trapping and storing CO2 and further reducing CO2 content in the atmosphere, but by then, much of the CO2 from 3 billion years earlier was already absorbed.
Tectonic forces do return some of this trapped gas back into the atmosphere, but over time, (I think - the articles on this seem both a little mixed and often complicated), but I think the tendency is for a planet with life on it, to gradually trap more and more of it's atmosphere leading not only to a decreasing CO2 content but also a lower atmospheric pressure over geological periods of time. One possible example of this is the Pterodactyl, which, in order to fly, it probobly would need a thicker atmosphere than we have today. Insects also tell us a bit about past atmospheric pressure. Insects don't have lungs, so their size is limited by the available oxygen that flows into their bodies through tracheae. Bigger insects imply 2 things, higher oxygen content and/or higher atmospheric pressure.
Now, more specifics and shorter term changes:
ItsMyPostAndIllWriteIfIWn, is correct about oceanic storage of atmospheric gases being affected by temperature, but I have a hard time seeing that as playing a major role on a geological scale, though it certainly has an effect on CO2 content today.
Major volcanic events, like the one 250 million years ago over Siberia or perhaps the one 66 million years ago over India might have burned sufficient coal and trapped carbon deposits to measurably change the atmosphere and CO2 content, but I think those changes were more temporary (though the one 250 million years ago was enormous, that might have made a significant longer lasting change).
Also natural disasters like the oceans growing stagnant and releasing H2S - which is very bad for life on land, or the oceans releasing huge amounts of CH4 would also have short term effects on atmospheric content - so there's a whole lot of moving parts to this question, depending on how close you want to look at it.
Footnote - I'm only a hobbyist, not a professor with a degree in this subject. It's a complicated field with a lot of moving parts.