Fifth force from Kaluza-Klein unification

Dilatonic dark matter and its experimental detection

“…This tells that the scale of the higher-dimensional gravitational constant G P need not be fixed by the Planck scale, because it is given by [1,11] …”

“…This confirms that when the internal space is of the Planck scale (i.e., when v 0 ≃ 1) the dilaton mass becomes of the Planck mass. But remarkably, a large v 0 naturally reduces the dilaton mass to the order of the elementary particle mass scale whenR G = 0 [1,11]. In fact (11) tells that the dilaton mass is determined by the scale of the internal space L G as follows,…”

“…At this point it is important to compare (6) and (11). Both provide a resolution of the hierarchy problem, but there are important differences.…”

The Equivalence Principle as a Symmetry

“…The first set comprises the Einstein equations G αβ = 8π T αβ , with T αβ given by (9). The second set comprises the conservation equations …”

“…Here as before Φ ≡ g αβ Φ ,α;β and some of the terms on the right-hand side are present in the energy-momentum tensor of (9). In fact, one can rewrite by the fifth dimension.…”