Abstract
In this paper we consider (n+1)-dimensional cosmological model with scalar field and antisymmetric (p+2)-form. Using an electric composite Sp-brane ansatz the field equations for the original system reduce to the equations for a Toda-like system with n(n−1)/2 quadratic constraints on the charge densities. For certain odd dimensions (D = 4m+1 = 5,9,13,...) and (p+2)-forms (p = 2m−1 = 1,3,5,...) these algebraic constraints can be satisfied with the maximal number of charged branes (i.e. all the branes have non-zero charge densities). These solutions are characterized by self-dual or anti-self-dual charge density forms Q (of rank 2m). For these algebraic solutions with the particular D, p, Q and non-exceptional dilatonic coupling constant λ we obtain general cosmological solutions to the field equations and some properties of these solutions are highlighted (e.g. Kasner-like behavior, the existence of attractor solutions). We prove the absence of maximal configurations for p = 1 and even D (e.g. for D = 10 supergravity models and those of superstring origin).
Highlights
C SISSA/ISAS 2004 http://jhep.sissa.it/archive/papers/jhep102004061 /jhep102004061 .pdf could be satisfied for certain “non-dangerous” intersection rules of the branes [12]
We consider the quadratic constraints for the charge densities of the branes. We find that these constraints have “maximal” solutions with all non-zero brane charge densities in particular odd dimensions with particular form fields: D = 5, 9, 13, . . . and p = 1, 3, 5 . . ., respectively
In this article we have examined a system where D = n+1 dimensional gravity was coupled to a scalar field plus a p + 2 rank form field
Summary
Where g = gMN dzM ⊗ dzN is the metric, φ is a scalar field, λ ∈ R is a constant dilatonic coupling and. Is a q-form, q = p + 2 ≥ 1, on a D-dimensional manifold M. Equations (2.4), (2.5) and (2.6) are, respectively, the multidimensional Einstein-Hilbert equations, the “Klein-Fock-Gordon” equation for the scalar field and the “Maxwell” equations for the q-form. The metric ansatz functions γ(u), φi(u), the scalar field φ(u) and the q-forms are assumed to depend only on u. < ik, we define a form of rank d(I) ≡ k τ (I) ≡ dyi1 ∧ . In [12] (see Proposition 2 in [12]) it was shown that the diagonal part of Einstein equations (2.4) and the equations of motion (2.5)–(2.6), for the ansatz given in (2.11), (2.17)–(2.19), are equivalent to the equations of motion for a 1-dimensional σ-model with the action (see [2, 3]).
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