Correspondence between n- and m-dimensional inflationary cosmologies

Details Correspondence between n- and m-dimensional inflationary cosmologies Correspondence between n- and m-dimensional inflationary cosmologies

Feb 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004phrvd..69d1302g&link_type=abstract

Physical Review D, vol. 69, Issue 4, id. 041302

Mathematics

Logic

2

Mathematical And Relativistic Aspects Of Cosmology, Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity

Scientific paper

It is shown that, from any n-dimensional Friedmann-Robertson-Walker (FRW) cosmology determined for a single scalar field minimally coupled to gravity, one can construct its m-dimensional counterpart, under the assumption of a common time coordinate and a structurally invariant scale factor for both spacetimes, by means of a simple algebraic correspondence relating gravitational constants and scalar field structural functions. If the considered cosmologies are supplemented with a perfect fluid, fitting a wide class of state equations of the form p+ρ=γf(ρ), then any n-dimensional FRW cosmology, coupled to a perfect fluid and a scalar field, possesses an m-dimensional counterpart, and vice versa. In particular, these assertions hold for single scalar field inflation models. A theorem on this respect is demonstrated. Various families of solutions are explicitly given and exhibit their correspondence with 3+1 cosmological spacetimes.

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