Pre-big bang collapsing universe from modern Kaluza-Klein theory of
  gravity
  We study the collapse of the universe described by a scalar field spherically
symmetric collapse of a system described by a massless scalar field from a 5D
Riemann-flat canonical metric, on which we make a dynamical foliation on the
extra space-like dimension. The asymptotic universe (absent of singularities)
results to be finite in size and energy density, with an vacuum dominated
equation of state. The important result here obtained is that the asymptotic
back-reaction effects are given by a negative constant: $1/2
[\frac{1}{1+\dot\psi^2}+\frac{1}{\dot\psi^2}]
<(\dot{\delta\bar{\phi}})^2>+{1\over 2a^2}
<(\vec{\nabla}\delta\phi)^2>|_{t\rightarrow\infty} = {-8 \Lambda_0 \over 3 \pi
G}$.
