Abstract
The present paper highlights an exotic universe having a metric which is partially suggested by the metric of an universe without time seen in [2]. The new metric is globally defined and depends on an exotic matter created by some classical waves. The massless scalar field (MSF) of this universe is also analyzed. Its existence depends on some constants k, k1 and k2, called MSF constants, which appear when we try to solve some ordinary differential equations deduced from the Klein-Gordon PDE attached to its metric. The MSF factor is the number α := −k1 + k2. We prove that the massless scalar field of this exotic universe exists if and only if α = 0.