I understand the basic theory of E Folds, but how was it discerned regarding our universe?
An "e-folding" is just an increase by a factor of e, the base of the natural logarithm. In cosmology, we often speak of e-foldings of expansion as a means of quantifying the amount of expansion before or after some event (e.g. the number of efolds before the end of inflation is a common time coordinate in inflation calculations). What specifically did you have a question about?
I am just trying to work out how scientist discovered that the universe expanded logarithmic ally.
What do you mean by "expanded logarithmically"? The use of the e-fold as a measure of the amount of expansion should not be taken to imply anything about the nature of the expansion. Since the universe has gone through many, many near-doublings in size since its beginning, the use of a logarithmic measure for the amount of expansion is especially convenient.
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