An Erlangen program for physics: a brief historical note for high school

Elmo Benedetto

University of Sannio

In this paper, I want to summarize the lecture notes prepared for my students of "De Luca" High School. One century is passed by the publication of General Relativity and this theory is considered by many physicists, mathematicians and philosophers the greatest triumph of human reason. Indeed, thanks to Einstein field equations, cosmology has been enclosed in the physical disciplines. Despite this, cosmology has still many unsolved problems. A cosmology without Einstein gravitational theory based on the Poincaré group of Special Relativity or based on an extension of relativistic group was developed in the twentieth century with two different approaches. It would be rather anachronistic to expect a similar approach to cosmology but, despite this, these theories are interesting from a historical point of view and they have become a source of new ideas in the context of modern physics. We want briefly to retrace the history from the beginning until today hoping to stimulate the curiosity of students and teachers. I hope that this manuscript can be a starting point to explore this topic.