Physics
Scientific paper
Jul 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phlb..174..251p&link_type=abstract
Physics Letters B, Volume 174, Issue 3, p. 251-256.
Physics
6
Scientific paper
The (4+N)-dimensional theory is considered whose lagrangian function is L4+N = √-ĝ αR2, where R is the Ricci scalar and α is a positive constant. The metric is ĝAB = diag(gab, φ-1g¯mn). Dimensional reduction leads to an effective four-dimensional lagrangian of induced-gravity type, ifL4 = √-g (κ1φ-(N-4)/2 + κ2φ-(N-2)/2 R + φ-N/2R2, where R is the four-dimensional Ricci scalar and κ1 and κ2 are constants. The positive semi-definiteness of L avoids the difficulties, pointed out recently by Horowitz and by Rubakov, which can arise in quantum cosmology when the (euclidean) action becomes negative. The compactification is onto a time-like internal space g¯mn, as suggested by Aref'eva and Volovich, giving a four-dimensional de Sitter space-time with φ = constant, which, however, is classically unstable on a time scale ~H-1. Decrease of the radius φ-1/2 of the internal space is ultimately halted by quantum effects, via some V(φ), and L4 then includes the usual Hilbert term and a cosmological constant.
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