Abstract

In this work we establish the correspondence between solutions to the Friedmann-Robertson-Walker cosmologies for perfect fluid and scalar field sources, where both satisfy state equations of the form p+p = ?f(?), not necessarily linear ones. Such state equations are of common use in the case of matter fluids; nevertheless, for a scalar field, they introduce relationships on the potential and kinetic scalar field energies which restrict the set of solutions. A theorem in this respect is demonstrated: From any given 3 + 1 cosmological solution, obeying the quoted state equations, one can derive its 2 + 1 cosmological counterpart or vice versa. Some applications are given. © 2003 The American Physical Society.