Physics – Nuclear Physics
Scientific paper
Sep 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989nuphb.324..187p&link_type=abstract
Nuclear Physics B, Volume 324, Issue 1, p. 187-204.
Physics
Nuclear Physics
15
Scientific paper
In a previous paper the quantum cosmology of the D-dimensional superstring theory was examined, retaining only the lowest-order terms in the effective lagrangian, namely the Ricci scalar R and the dilaton field π. The (anisotropic) mini-superspace approximation was employed, the interval being ds2 = dt2 - a2(t)dx2 - b2(t)dy2, where t is comoving time, a(t) ≡ eα(t) is the scale factor of the M-dimensional physical space dx2 and b(t) ≡ eβ(t) is the scale factor of the N-dimensional internal space dy2, where D = M + N + 1. The Wheeler-DeWitt equation for the wave function of the universe Ψ was derived, and it was found that Ψ was a constant in the ``no-scale'' metric for which α = -β, provided that (M - N)2 = M + N (eq. (1)). This condition requires that (D - 1) must be a perfect square. It allows the cases both of the bosonic string (D = 26, M = 10, N = 15) and the superstring (D = 10, M = 3, N = 6), as well as the original Kaluza-Klein theory (D = 5, M = 3, N = 1).
The analysis is extended here to include the effects of higher-derivative terms α'R2, where α' is the string slope parameter (the string tension being T = 1/2πα'). The Wheeler-DeWitt equation for the bosonic string and for the superstring is derived as a Schrödinger equation, and it is explained why no corresponding equation can be derived for the heterotic string, at this level of approximation. The question is raised, why the expansion of the universe at the onset of the classical era is anisotropic rather than isotropic. The Schrödinger equation contains a ``potential'' V(α, β αdot, βdot), which, to lowest order in α', vanishes in the ``no-scale'' metric, provided that eq. (1) holds, but is positive definite in the isotropic space-time, for which α = β. The anisotropic solution is thus associated with a lower energy, and may be favoured for this reason.
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