Abstract
The problem of incompatible orders of magnitude for quantum vacuum energy certainly stems from quantum gravity, which is still misunderstood. Physicists have been trying to build a quantum theory of gravity for over century, but without success. Since quantum field theory, the strong, weak and electromagnetic forces have been unified. One such attempt is string theory. For forty years, it has been replacing particle singularities with one-dimensional elements (of size 10-35 m). But it requires additional dimensions of space, 26 in some cases, and 10 if there is supersymmetry between fermions of bosons, and a whole class of supersymmetric particles to be assumed beyond the standard model of elementary particles. In this unification of forces, gravity would also have its interaction boson - the graviton - and we could imagine the addition of a small-scale Yukawa potential. It is therefore essential to test the law of gravity on a small scale.
Increasingly precise experiments, in common with Casimir force measurements, have yet to produce any deviations. Tests of the equivalence principle (EP) and the universality of free fall (UFF) are reviewed from the Eötvös experiment to the Microscope satellite successfully launched in April 2016. More than ten orders of magnitude have been gained. Some aspects of string theory are discussed, in particular its aspect of renormalizing infinities (gravity is not renormalizable in field theory). Several string theories existed until 1995, when M-theory unified the five string theories, with ten dimensions. Quantum states can be described with D-branes, or surfaces included in the eleven-dimensional Universe of supergravity. Observations of the microwave background, a remnant of the Big Bang, provide numerous constraints on the nature of dark energy. Although dark energy is negligible at t = 380 000 years, we can use the gravitational lensing effects of the cosmological background by the structures of the Universe, between z = 1 000 and z = 0, and prove the existence of dark energy, only with the CMB background.
