Research can be used as an uncountable noun for the general body of information on a topic. Alternatively, you could be referring to a specific study/work, which would then be used with the article.
Research suggests that the increase will continue for the next several years
The research of Dr Smith indicate that the situation will resolve itself by next year
For your examples, depending on the specific context, either could be correct.
According to the research, there is [an] increase in market cap.
Would be more typical if the work referred to a specific scope of research (the work of a particular person, university, a single study, etc).
According to research, there is [an] increase in market cap.
Would be more typical if the work is referring to research as an abstract quality.