A Plane Symmetric Cosmological Model

Abstract

A plane symmetric perfect fluid cosmological model has been derived from class-one considerations- The pressure and density are found to be decreasing functions of time and lines of flow are geodesies. The coordinate system used turns out to be a co-moving system. The spatial cross-section of the universe at any given instant of time is flat. When the model represents a universe filled with disordered radiation it reduces to a particular case of the Lemaître universe. From the consideration of geodesic deviation we conclude that the Universe is expanding with time. The fourteen scalar invariants of the second order for the line-element have been evaluated and it is found that only two of them are independent. The Lemaitre universe is conformal to flat space-time while this model is not so in general and hence it is not a special case of the Lemaître universe. The line-element admits a four-parameter group of motions.