Why use "the" in "than the 3.5bn years ago"?
Solution 1:
The reason for "the" is that this refers to a particular 3.5 bn year limit, i.e. the specific one that was mentioned in the previous research.
You may object that there aren't distinct 3.5 bn years ago eras - there can only be one. Logically that is true but sometimes usage overrides logic.
So we could say
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3.5 billion years ago, there was volcanic activity on the Moon.
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3.5 billion years ago, the first signs of life appeared on Earth.
These are independent statements so we could talk about "the 3.5 billion years ago that there was volcanic activity" and "the 3.5 billion years ago that there was life on Earth".
The reason we can refer to them in this way might be because they are both estimates and one might be a much more accurate estimate than the other, so they are in some way distinct.
Solution 2:
This is so because "3.5 bn years" is determined by the that-clause (that is the estimate derived…) and that it is a unique possibility.
- This is not the bundle (that) they showed to you. (unique)
- This is not a bundle (that) they showed to you. (not unique)
The determination can result from other circumstances.
- This is during the first hour on the job. It is for the second hour that you need to use new tools.
Addition prompted by user Jack Rowntree's answer
In my opinion, Jack Rowntree does detect a problem in the formulation of the proposed sentence, and if I failed to give sufficient thought to it as I read the sentence, I feel now that his remarks make it stand out enough to address it, which I wouldn't have done had I not disagreed to a certain extent with him.
This number of years is a means to define a date; a point in time is what we have to specify since the key word is "until"; we do that not by means of a date since for such times way back in the geological times and still further back, dates are rather meaningless, unless it would be rather that there is no established usage; instead it is done by means of a span of time with the convention that the inferior limit of that span is the point or date referred to; however, in order to establish a correspondence in time for that inferior limit the superior limit must be fixed. You can fix it in several ways, by choosing a reference point, an event, a period if an approximate date is sufficient. Here, this is accomplished by a reference to the present in general (which is again an approximation but sufficiently good since even several decades do not matter in this question); the term to fix that reference is "ago". As Jack Rowntree notices the formulation is unusual or at least it doesn't have the feel of proper syntax. This is correct in my opinion since the term in the comparison is not a simple term but "3.5 bn years ago"; as "the" does not bear upon "ago" there is not a well defined term for the comparison; this is highlighted in Jack Rowntree's answer. As he shows, an apparent solution is to suppress "ago".
- Researchers hope rocks collected here will confirm that volcanic activity on the Moon continued until far more recently than the 3.5bn years that is the estimate derived from studies of currently available samples.
However, that does not define a date but a span of time and this is not proper. If keeping the article, the only way out towards normal syntax is in an addition of terms.
- Researchers hope rocks collected here will confirm that volcanic activity on the Moon continued until far more recently than the point 3.5bn years ago, that is the estimate derived from studies of currently available samples.
There is also, according to Jack Rowntree the possibility of doing away with the article and I agree entirely with that.
- Researchers hope rocks collected here will confirm that volcanic activity on the Moon continued until far more recently than 3.5bn years ago, (that/which) is the estimate derived from studies of currently available samples.