Could anyone explain to me what f(R) gravities are in simplest terms?

Answer 1

f(R) gravities are those where the distance aspects of space-time (the metric) and the connection aspects (the curvature) are dealt with symmetrically. In one place, a function of the curvature f(R) replaces a term with just R. It is claimed by those doing f(R) theories that they avoid many of the problems of general relativity including such things as 'dark matter'. Unfortuantely, they have very little motivation other than as a formal possible modification of the laws of gravity. They are being actively investigated at this point.

Answer 2

Sorry, you could please say what you mean by f(R) gravities?