Dynamics of the scalar field in 5-dimensional Kaluza-Klein theory
  Using the language of differential forms, the Kaluza-Klein theory in 4+1 dimensions is derived. This theory unifies electromagnetic and gravitational interactions in four dimensions when the extra space dimension is compactified. Without any ad-hoc assumptions about the five-dimensional metric, the theory also contains a scalar field coupled to the other fields. By a conformal transformation the theory is transformed from the Jordan frame to the Einstein frame where the physical content is more manifest. Including a cosmological constant in the five-dimensional formulation, it is seen to result in an exponential potential for the scalar field in four dimensions. A similar potential is also found from the Casimir energy in the compact dimension. The resulting scalar field dynamics mimics realistic models recently proposed for cosmological quintessence. 
Ingunn Kathrine Wehus and Finn Ravndal