Primordial fluctuations of scale factor in closed Universe in
  Einstein$-$Cartan gravity
  We consider a homogeneous and isotropic Universe, described by the
minisuperspace Lagrangian with the scale factor as a generalized coordinate. We
show that the energy of a closed Universe is zero. We apply the uncertainty
principle to this Lagrangian and propose that the quantum uncertainty of the
scale factor causes the primordial fluctuations of the matter density. We use
the dynamics of the early Universe in the Einstein$-$Cartan theory of gravity
with spin and torsion, which eliminates the big-bang singularity and replaces
it with a nonsingular bounce. Quantum particle production in highly curved
spacetime generates a finite period of cosmic inflation that is consistent with
the Planck satellite data. From the inflated primordial fluctuations, we
determine the magnitude of the temperature fluctuations in the cosmic microwave
background, as a function of the numbers of the thermal degrees of freedom of
elementary particles and the particle production coefficient, which is the only
unknown parameter.
