There is no gravitational force in Nature
The experimental success of Einstein's general relativity provided one of the most certain pieces of foundational knowledge - that no gravitational force is involved in gravitational phenomena.
This is an exemplary piece of foundational knowledge because it will never be challenged by future experiments for an obvious reason: as experiments do not contradict one another, no future experiment will contradict the experimental fact that particles do not resist their fall (i.e. their apparent acceleration) , which means that no gravitational force is causing their fall (and therefore they move by inertia).
Two things should be emphasized as strongly as possible:
This experimental fact (which reflects Einstein's "happiest thought" of his life ) is captured by the geodesic principle in general relativity, which is regarded as "a natural generalization of Newton's first law" , that is, "a mere extension of Galileo's law of inertia to curved spacetime" .
Making use of this firmly established piece of foundational knowledge has an immediate impact on fundamental research in gravitational physics in two directions:
1. It rules out any alternative theories of gravity and any attempts to quantize gravity (by proposing alternative representations of general relativity aimed at making it amenable to quantization) that regard gravity as a physical field which gives rise to a gravitational force. For instance, papers or grant proposals (dealing with modified theories of gravitation that involve a gravitational force) should be rejected right away since they ultimately contradict the experimental evidence (especially if they do not even mention how that evidence is accounted for).
2. The implications of the fact that gravitational force does not exist for general relativity itself should be examined critically and rigorously in order to determine whether presently adopted notions represent real features of the world (and, if not, they should be excluded from the physical knowledge) - e.g., the status of gravitational energy and momentum in general relativity should be clarified (as there is no gravitational force, how can there be gravitational energy since such energy is defined as the work done by gravitational forces; regarding gravitational energy as nonlocal is not immune from facing this question).
 A falling accelerometer, an example of real experiments, does prove that no gravitational force is acting on the accelerometer: the absolute (frame-independent) fact is that the accelerometer reads zero acceleration, that is, zero resistance to its fall and therefore zero gravitational force acting on it. The accelerometer's apparent acceleration is not true acceleration (which is an absolute, i.e., frame-independent, property in both special and general relativity).
 Einstein called the "happiest thought" of his life the following insight (most probably in November 1907), which helped him make a gigantic step toward the new understanding of gravitation :
I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me: "If a person falls freely he will not feel his own weight." I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.
 A. Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, Oxford 2005) p. 179.
 J. L. Synge, Relativity: the general theory. (Nord-Holand, Amsterdam 1960) p. 110.
 W. Rindler, Relativity: Special, General, and Cosmological (Oxford University Press, Oxford 2001) p. 178.