# Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model

• We investigate a 6D generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. Each stress-energy tensor $T_{ab}^{i}$ on the brane is shown to be similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model, in which each 3-brane Lagrangian yielded a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5D Friedmann-Robertson-Walker field equations. In a slightly later period, the expansion of the universe is proportional to the square root of time, $t^{\frac{1}{2}}$, which is similar to the period of the radiation-dominated regime. Moreover, we investigate the case with two $a(t)$ and two $b(t)$. In a large range of $t$, we obtain the 3D effective cosmological constant $\Lambda_{\rm eff} = -2\Omega/3>0$, which is independent of the integral constant. Here, the scale factor is an exponential expansion, which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model that solves the dark energy problem, while guaranteeing a positive brane tension.
•  [1] Th. Kaluza, Sitzungseber. Press. Akad. Wiss. Phys. Math. K-lasse 996 (1921); O. Klein, Z. Phys., 37: 895 (1926); Nature(London) 118: 516 (1926) [2] N. Arkani-Hamed, S. Dimopoulos, and G.Dvali, Phys. Lett. B, 429: 263 (1998) doi: 10.1016/S0370-2693(98)00466-3 [3] N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. Rev. D, 59: 086004 (1999) doi: 10.1103/PhysRevD.59.086004 [4] R. Sundrum, Phys. Rev. D, 59: 085009 (1999) doi: 10.1103/PhysRevD.59.085009 [5] J. Lykken, L. Randall, J. High Energy Phys., 06: 014 (2000) [6] I. Antoniadis, Phys. Lett. B, 246: 377 (1990) doi: 10.1016/0370-2693(90)90617-F [7] I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos et al, Phys. Lett. B, 436: 257 (1998) doi: 10.1016/S0370-2693(98)00860-0 [8] J. Polchinski, String Theory. Vol. 2: Superstring theory and beyond, (Cambridge University Press, 1998) [9] L. Randall and R. Sundrum, Phys. Rev. Lett., 83: 3370 (1999) doi: 10.1103/PhysRevLett.83.3370 [10] E. K. Park and P. S. Kwon, Phys. Rev. D, 82: 046001 (2010) [11] S. Das, D. Maity, and S. Sengupta, J. High Energy Phys., 05: 042 (2008) [12] R. Koley, J. Mitra, and S. SenGupta, Phys. Rev. D, 92(R): 041902 (2009) [13] C. P. Burgess, F. Quevedo, G. Tasinato et al, J. High Energy Phys., 11: 069 (2004) [14] H. P. Nilles, A. Papazoglou, and G. Tasinato, Nucl. Phys. B, 677: 405 (2004) doi: 10.1016/j.nuclphysb.2003.11.003 [15] M. Sasaki, T. Shiromizu, and K.-i. Maeda, Phys. Rev. D, 62: 024008 (2000) doi: 10.1103/PhysRevD.62.024008 [16] J. Mitra, T. Paul, and S. SenGupta, Eur. Phys. J. C, 77: 833 (2017) doi: 10.1140/epjc/s10052-017-5420-6 [17] S. Chakraborty, S. SenGupta, Eur. Phys. J. C, 75(11): 538 (2015) doi: 10.1140/epjc/s10052-015-3768-z [18] I. Banerjee, S. Chakraborty, and S. SenGupta, Phys. Rev. D, 99: 023515 (2019) doi: 10.1103/PhysRevD.99.023515 [19] S. Chakraborty and S. SenGupta, Phys. Rev. D, 92: 024059 (2015) doi: 10.1103/PhysRevD.92.024059 [20] S. Chakraborty and S. SenGupta, Eur. Phys. J. C, 76: 552 (2016) doi: 10.1140/epjc/s10052-016-4394-0 [21] S. Perlmutter et al, Astrophys. J., 517: 565 (1999) doi: 10.1086/apj.1999.517.issue-2 [22] A. Riess et al, Astron. J., 116: 1009 (1998) doi: 10.1086/300499 [23] C. L. Bennett et al, Astrophys. J. Suppl. Ser., 148: 1 (2003) doi: 10.1086/apjs.2003.148.issue-1 [24] C. B. Netterfield et al, Astrophys. J., 571: 604 (2002) doi: 10.1086/apj.2002.571.issue-2 [25] N.W. Halverson et al, Astrophys. J., 568: 38 (2002) doi: 10.1086/apj.2002.568.issue-1 [26] C. A. Middleton and E. Stanley, Phys. Rev. D, 84: 085013 (2011) doi: 10.1103/PhysRevD.84.085013 [27] A. Karch and L. Randall, J. High Energy Phys., 05: 008 (2001) [28] Z. C. Wu, Phys. Rev. D, 80: 105001 (2009) doi: 10.1103/PhysRevD.80.105001

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## Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model

###### Corresponding author: Guang-Zhen Kang, gzkang@nju.edu.cn
• 1. School of Science, Yangzhou Polytechnic Institute, Yangzhou 225127, China
• 2. Department of Physics, Nanjing University, Nanjing 210093, China
• 3. School of Science, Changzhou Institute of Technology, Changzhou 213032, China
• 4. School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China
• 5. Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing 210093, China
• 6. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing 100190, China

Abstract: We investigate a 6D generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. Each stress-energy tensor $T_{ab}^{i}$ on the brane is shown to be similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model, in which each 3-brane Lagrangian yielded a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5D Friedmann-Robertson-Walker field equations. In a slightly later period, the expansion of the universe is proportional to the square root of time, $t^{\frac{1}{2}}$, which is similar to the period of the radiation-dominated regime. Moreover, we investigate the case with two $a(t)$ and two $b(t)$. In a large range of $t$, we obtain the 3D effective cosmological constant $\Lambda_{\rm eff} = -2\Omega/3>0$, which is independent of the integral constant. Here, the scale factor is an exponential expansion, which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model that solves the dark energy problem, while guaranteeing a positive brane tension.

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