A uniform, isotropic cosmological model filled by scalar and pseudosca
lar fields subject to chiral symmetry is described. The model is nonsi
ngular, topologically compact, and possesses particlelike properties.
Space-time is two-sheeted. The model is doubly-connected and CPT invar
iant. it consists of two pulsating universes (world and antiworld). Th
e dynamical K entropy resulting from the instability of the initial st
ate of the fields and the double-connectedness of the model is calcula
ted. Scalar gravitational perturbations can form periodic structures i
n the spatial distribution of the effective energy density of the fiel
ds, since the spatial scales of the perturbations are commensurate. St
ructures of this kind may be responsible for the periodic distribution
of distant astronomical objects.