To some extent, it is a matter of style. The author likes that word better.
There are, however differences between those words.
Awareness has inflections that relate to perception*: I'm aware of something if I can see, hear, smell, touch or taste it. You can be aware of something and not know very much about it.
Knowledge is an intellectual attribute and includes facts and information that have been acquired*. You can know facts about a subject, yet still not have a real cognizance of it.
Cognizance relates to formal knowledge and comes from the Latin root, to learn*.
So, in terms of its 'perception' meaning, awareness is not nearly distinct enough from feeling and the distinction is what the author is trying to highight. The word awareness would not convey the correct meaning in this instance.
The knowledge vs cognizance issue isn't quite as obvious, but essentially, you can know about feelings (or 'the realm of feeling') without understanding it, and simple knowledge isn't quite what the author is trying to convey. He is talking about knowledge with understanding and so has opted for cognizance which carries that meaning better.
Other words which would also have worked (ie carried the full meaning of cognizance) include: understanding, comprehension and possibly perspicacity (though the last relates more to the ability of the person to understand than to the subject being understood).
A suggestion: Don't just look at Google results for 'define wordOfInterest' when you are trying to understand subtleties between word choices. Check multiple online (and/or hardcopy) dictionaries in both US and UK English to give yourself the best chance of understanding (or becoming cognizant).
* Definitions from Oxford Dictionaries.