Relationship between (2 + 1) and (3 + 1)-Friedmann Robertson Walker cosmologies; linear, non-linear, and polytropic state equations

Details Relationship between (2 + 1) and (3 + 1)-Friedmann Robertson Walker cosmologies; linear, non-linear, and polytropic state equations Relationship between (2 + 1) and (3 + 1)-Friedmann Robertson Walker cosmologies; linear, non-linear, and polytropic state equations

Apr 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005gregr..37..685g&link_type=abstract

General Relativity and Gravitation, Volume 37, Issue 4, pp.685-711

Mathematics

Logic

Exact Solutions, Cosmology, Inflation

Scientific paper

It is shown that Friedmann Robertson Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ρ = γ f(ρ). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form pφ+ρφ = γρφβ are reported, in particular Barrow Saich, and Barrow Burd Lancaster Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.

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