Cosmological perturbations in the (1+3+6)-dimensional space-times

الأصل · EN

Cosmological perturbations in the (1+3+6)-dimensional space-times including photon gas without viscous processes are studied on the basis of Abbott et al.'s formalism. Space-times consist of the outer space (the 3-dimensional expanding section) and the inner space (the 6-dimensional section). The inner space expands initially and contracts later. Abbott et al. derived only power-type solutions in the small wave-number limit which appear at the final stage of the space-times. In this paper, we derive not only small wave-number solutions, but also large wave-number solutions. It is found that the latter solutions depend on the two wave-numbers kᵣ and kᵣ (which are defined in the outer and inner spaces, respectively), and that the kᵣ-dependent and kᵣ-dependent parts dominate the total perturbations when (kᵣ/r(t))/(kᵣ/R(t)) >> 1 or << 1, respectively, where r(t) and R(t) are the scale-factors in the outer and inner spaces. By comparing the behaviors of these perturbations, moreover, changes in the spectrum of perturbations in the outer space with time are discussed.