The phrase "reigning theory" refers to the current or popular belief or idea that has the most influence or control over a particular subject or field. It is the dominant theory at a given point in time. Full definition
New experiments provide an alternative to a long - reigning theory of the way we form memories of experiences (scientificamerican.com)
The Higgs boson was the last particle predicted by the reigning theory in particle physics: the standard model. (businessinsider.com)
If physicists can't agree on — or don't know — what their reigning theory is all about, does it mean they've hit a wall in terms of understanding the world? (discovermagazine.com)