Narrow Results

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.

We discuss multi-field models of inflation, such as the curvaton, modulated reheating scenario, as the origin of density fluctuations. After summarizing the current status of such models from the viewpoint of observations of the scalar spectral index, the tensorto- scalar ratio and so on, we investigate the CMB spectral μ distortion in such a model, which captures the property of density fluctuations on small scales. We find that, given the current constraint on the spectral index and the tensor-to-scalar ratio, the predicted distribution of the value of μ in multi-field models could be broader than that in the standard single-field inflation model and larger values of μ could be realized. Some issues of isocurvature fluctuations in multi-field models are also discussed.