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In this work we establish the correspondence between solutions to theFriedmann--Robertson--Walker cosmologies for perfect fluid and scalar fieldsources, where both ones fulfill state equations of the form $p+\rho=\gammaf(\rho)$, not necessarily linear ones. Such state equations are of common usein the case of matter--fluids, nevertheless, for a scalar field, they introducerelationships on the potential and kinetic scalar field energies which restrictthe set of solutions. A theorem on this respect is demonstrated: From any given(3+1)--cosmological solution, obeying the quoted state equations, one canderive its (2+1)--cosmological counterpart or vice-versa. Some applications aregiven.Comment: 5 pages, Latex, accepted in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Relationship between<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>Friedmann-Robertson-Walker cosmologies

Relationship between2+1and3+1Friedmann-Robertson-Walker cosmologies