We consider an inflationary scenario in the holographic braneworld with a cosmological fluid occupying the 3+1 dimensional brane located at the holographic boundary of an asymptotic ADS$_5$ bulk. The contribution of the boundary conformal field can be represented as a modification of Einstein's equations on the boundary. Using these effective Einstein equations we calculate the cosmological perturbations and derive the corresponding power spectra assuming a general $k$-essence type of inflaton. We find that the braneworld scenario affects the scalar power spectrum only in the speed of sound dependence on the slow-roll parameters whereas there is no change in the tensor power spectrum. This implies that the changes in the spectral indices appear at the second order in the slow-roll parameter expansion.

中文翻译：

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全息宇宙学中的原始扰动和暴胀

我们考虑了全息膜世界中的暴胀情景，其中宇宙流体占据了位于渐近 ADS$_5$ 体全息边界的 3+1 维膜。边界共形场的贡献可以表示为对边界上的爱因斯坦方程的修改。使用这些有效的爱因斯坦方程，我们计算宇宙学扰动并推导出相应的功率谱，假设一般的暴胀子本质类型是 $k$。我们发现，膜世界场景仅在依赖于慢滚参数的声速方面影响标量功率谱，而张量功率谱没有变化。这意味着光谱指数的变化出现在慢滚参数扩展中的二阶。