Elementary particle physics has demonstrated the complete symmetry between particles and antiparticles. From this follows the equivalence between matter and antimatter. It is very unsatisfactory that current cosmological theories are not symmetric with respect to matter and antimatter.

It is postulated that a cosmological theory should be matter-antimatter symmetric, and introduce no ad hoc laws of nature. These postulates form part of Klein's theory, but are not satisfied by the "expanding universe" or "continuous creation" theories.

Essential properties of an "ambiplasma" consisting of matter and antimatter are studied. It is shown that it emits radio waves but no detectable $\gamma$ rays. If initially the plasma contains equal amounts of matter and antimatter, the two ingredients can be separated by electromagnetic and gravitational forces. In the present state of the universe there may be coexisting regions of matter and antimatter, separated by thin "Leidenfrost" layers.

Klein's theory of the metagalaxy is reviewed and developed. The "initial condition" is supposed to be an extremely thin plasma of matter and antimatter which contracts under the action of gravitation. When the density has reached about ${10}^{-2\mathrm{}}$ particles ${\mathrm{cm}}^{-3\mathrm{}}$, annihilation produces a radiation pressure which transfers the contraction to the present expansion. The theory leads to a relation between the average density and the Hubble parameter which is in satisfactory agreement with observations.

Different ways of detecting antimatter are discussed. It is possible that radio stars consist of ambiplasma. The enormous energy quantities emitted from some celestial objects may be supplied by annihilation.

Outside our metagalaxy there may exist other similar systems. The possibility of observing them is discussed.

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