Curvature Perturbation and Domain Wall Formation with Pseudo Scaling Scalar Dynamics

Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation and if $n$ is larger it obeys a scaling solution without oscillation. We study in detail the case where $n$ is equal to the critical value, and find a peculiar scalar dynamics which is neither oscillating nor scaling solution, and we call it a pseudo scaling solution. We also discuss cosmological implications of a pseudo scaling scalar dynamics, such as the curvature perturbation and the domain wall problem.