From Quantum Correlations to Inflationary Tracking Scalar Field Evolution

The tracking condition $\dot{\phi}^2=\gamma H^{-m}$ for single scalar field theory leads to analytic inflationary solutions, which are compatible with the current cosmic microwave background radiation experiments. To our knowledge this is the only analytic solution of inflation which is compatible with the data, to date. In this work we seek for some theoretical basis that can lead to the tracking condition $\dot{\phi}^2=\gamma H^{-m}$. As we show, if the Universe is seen pre-inflationary as a quantum statistical system, the scalar field may emerge as a collective condensate of the quantum degrees of freedom. In the quantum-to-classical transition of the Universe, the scalar field two point function yields the susceptibility of the theory with an inherent correlation length. Using information theoretic motivation and Wilsonian quantum field theoretic arguments, we demonstrate that the tracking conditions $\dot{\phi}^2=\gamma H^{-m}$ emerge from this framework.