Generalized Approach for the Perturbative Dynamical Braneworld in D dimensions
arxiv(2023)
摘要
In this paper, we propose an approach to derive the brane cosmology in the
D-dimensional braneworld model. We generalize the "bulk-based" approach by
treating the 4-brane as a small perturbation to the D-dimensional spherically
symmetric spacetime. The linear corrections from a static 4-brane to the metric
are derived from the linearized perturbation equations, while the nonlinear
corrections are found by a parameterization of the perturbed metric solution.
We use a time-dependent generalization to give the nonlinearly perturbed metric
solution for the dynamical braneworld model, and analyse the stability of the
model under the motion of the 4-brane. Through the fine tuning, we can recover
the Friedmann equations for the universe with and without an effective
cosmological constant. More importantly, the de Sitter expansion of the
universe can be reproduced.
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