Astrophys Space Sci (2006) 306:269–272 DOI 10.1007/s10509-006-9272-z ORIGINAL ARTICLE Non-Existence of Five Dimensional Perfect Fluid Cosmological Model in Lyra Manifold G. Mohanty · K. L. Mahanta · R. R. Sahoo Received: 13 May 2006 / Accepted: 2 November 2006 C  Springer Science + Business Media B.V. 2006 Abstract In this paper we have taken an attempt to con- struct a five dimensional perfect fluid cosmological model within the framework of Lyra manifold. It is found that nei- ther perfect fluid nor dust distributions survive. Finally the exact solutions of the vacuum field equations are obtained. Keywords Five dimension . Perfect fluid . Lyra manifold 1 Introduction The unification of gravitational forces with other forces in nature is not possible in the usual four-dimensional space- time. So in higher dimensional quantum field theory this may be possible (Appelquist et al., 1987; Weinberg, 1986; Chodos and Detweler, 1980). This idea is important in the field of cosmology, as we know that the universe was much smaller in the early stage of the evolution than today. So we predict that the present four-dimensional space-time of the universe could have preceded by a higher dimensional space- time. The extra dimensions reduced to a volume of the order of the Planck length with the passage of time, which are not observable at the present stage of the universe. Freund (1982), Appelquist and Chodos (1983), Randjbar Daemi et al. (1984), Rahaman et al. (2002a) and Singh et al. (2004) claimed through the solutions of the field equations that there is an expansion of four dimensional space time while fifth dimension contracts or remains constant. Further Guth (1981) and Alvarez and Gavela (1983) observed that during contraction process extra dimensions produce large G. Mohanty · K. L. Mahanta · R. R. Sahoo () P.G. Department of Mathematics, Sambalpur University, Jyoti Vihar-768019, Orissa, India e-mail: rakesh.s24@gmail.com amount of entropy, which provides an alternative resolution to the flatness and horizon problem, as compared to usual inflationary scenario. It is found in the literature (Ellis, 1979; Misner, 1968; Hu, 1983) that bulk viscosity could arise in many circumstances and could lead to the mechanism of galaxy formation during the evolution of the universe. In order to obtain a static model of the universe, Einstein introduced the cosmological constant into his field equations. Without the cosmological term his field equations admit only non-static cosmological models for non-zero energy density. Weyl (1918) proposed a modification of Riemannian man- ifold in order to geometrize the whole of gravitation and electromagnetism. His theory is found to be physically un- satisfactory. Later another modification of Riemannian ge- ometry proposed by Lyra (1951) bears close resemblance to Weyl’s geometry. Sen (1957) showed that the static model with finite density in Lyra manifold is similar to the static model in Einstein theory. Subsequently Halford (1970) stud- ied cosmological theory within the framework of Lyra’s ge- ometry and pointed out that the vector field φ i in Lyra’s geometry plays similar role of cosmological constant  in general theory of relativity. Further, he suggested that en- ergy conservation law does not hold in the cosmological the- ory based on Lyra’s geometry and he developed a theory within the framework of Lyra’s geometry which gives rise to non-static perfect fluid models. Halford (1972) showed that the scalar tensor theory of gravitation in Lyra manifold predicts the same effects, within observational limits, as in the Einstein theory. Soleng (1987) obtained that the constant gauge vector φ in Lyra’s geometry includes either a creation field and be equal to Hoyle’s (1948) creation field cosmol- ogy or contains a special vacuum field, which together with the gauge vector may be considered as a cosmological term. In the latter case the solutions of field equations are same to those of general theory of relativistic cosmologies with a Springer