We obtain a novel model of oscillating non-singular cosmology on the spatially flat Randall–Sundrum (RS) II brane. At early times, the universe is dominated by a scalar field with an inflationary emergent potential \(V(\phi )=A(e^{B\phi }-1)^2\), A and B being constants. Interestingly, we find that such a scalar field can source a non-singular bounce, replacing the big bang on the brane. The turnaround again happens naturally on the brane dominated by a phantom dark energy [favoured by observations (Knop et al. in Astrophys J 598:102, 2003. Spergel et al. in Astrophys J Suppl 148:175, 2003. Tegmark et al. in Phys Rev D 69:103501, 2004) at late times], thus avoiding the big rip singularity and leading upto the following non-singular bounce via a contraction phase. There is a smooth non-singular transition of the brane universe through both the bounce and turnaround, leading to alternate expanding and contracting phases. This is the first model where a single braneworld of positive tension can be made to recycle as discussed in details in the concluding section.

我们在空间平坦的 Randall-Sundrum (RS) II 膜上获得了一种新颖的振荡非奇异宇宙学模型。早期，宇宙由标量场主导，具有暴胀涌现势\(V(\phi )=A(e^{B\phi }-1)^2\)，A和B为常数。有趣的是，我们发现这样的标量场可以产生非奇异反弹，取代膜上的大爆炸。这种转变再次自然地发生在由幻影暗能量主导的膜上[受到观察的青睐（Knop 等人，在《天体物理学杂志》 598:102, 2003 年。Spergel 等人，在《天体物理学杂志增刊》148:175, 2003 年。Tegmark 等人，2003 年。）在Phys Rev D 69:103501, 2004）后期]，从而避免了大撕裂奇点并通过收缩阶段导致接下来的非奇点反弹。通过弹跳和周转，膜宇宙有一个平滑的非奇异过渡，导致交替的膨胀和收缩阶段。这是第一个模型，其中可以使正张力的单个膜世界进行回收，如结论部分详细讨论的。