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Dynamical codimension-2 brane in a warped six dimensional space-time

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In this paper we present the Einstein equation extended in six-dimensions (6D) from the formalism of codimension-2 brane, which is created by a 4-brane and 4-anti brane moving in the warped 6D bulk space-time. The system of equations of motion for the dynamical codimension2 brane has been derived to describe the cosmological evolution on the probe branes. Some cosmological consequences are investigated. | Communications in Physics, Vol. 28, No. 3 (2018), pp. 277-285 DOI:10.15625/0868-3166/28/3/12583 DYNAMICAL CODIMENSION-2 BRANE IN A WARPED SIX DIMENSIONAL SPACE-TIME PHAN HONG LIEN † Le Quy Don Academy of Technology, 236 Hoang Quoc Viet, Hanoi, Vietnam † E-mail: phlien.mta@gmail.com Received 9 May 2018 Accepted for publication 1 August 2018 Published 31 August 2018 Abstract. In this paper we present the Einstein equation extended in six-dimensions (6D) from the formalism of codimension-2 brane, which is created by a 4-brane and 4-anti brane moving in the warped 6D bulk space-time. The system of equations of motion for the dynamical codimension2 brane has been derived to describe the cosmological evolution on the probe branes. Some cosmological consequences are investigated. Keywords: six-dimensions (6D), codimension-2 brane, Schwarzschild AdS (SAdS6 ). Classification numbers: 98.80.-k; 11.30.Rd. I. INTRODUCTION Besides the extended models of Standard Model (SM) and Standard Cosmology, the extra dimensions have been considered as the ways to investigate both old and open problems of Particle physics and Cosmology, in the new physics beyond the SM to unify gravity with gauge interactions [1–3]. Particularly, in the brane-world theories, the D-brane inflation in warped compactification has attracted much attention recently [4, 6]. In that case, the inflation is identified as the separation between a brane and an antibrane, which is described by codimension-2 brane coupled to bulk metric [7, 8]. In this paper we consider the time and external spatial-dependent dimensions in a warped six-dimensional bulk. Based on the form of the brane-world energy momentum tensor proposed by Shiromizu et al. in five dimensions (5D) [9], the theory to the codimension-2 brane was extended to six dimensions (6D). Here 4-brane and 4-anti brane have been assumed to be an Anti de Sitter (AdS) space. The Einstein equations in 6D show that the velocities, the curvature and the geometry of .