Hyperbolic geometry of cosmological attractors
Hyperbolic geometry of cosmological attractors
复制标题
宇宙吸引子的双曲几何
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
D. Roest
中科院分区：
文献类型：
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作者：
J. J. Carrasco;R. Kallosh;Andrei Linde;D. Roest
宇宙α吸引子对普朗克测量的暴胀谱指数n(s)给出了一个自然的解释，同时预测了张量与标量之比r的范围，与所有观测结果一致，将在未来的b模实验中更精确地测量。我们强调了庞加莱盘或半平面的双曲几何在超重力构造中的关键作用。这些几何形状在莫比乌斯变换下是等距的，其中包括膨胀场的位移对称。我们引入了一个新的卡勒势框架，它明确地保持了这种对称性，使暴胀成为轻的。此外，我们还包括了高阶曲率变形，它可以稳定一个与暴胀轨迹正交的方向。我们通过稳定单个超场吸引子来说明这个新框架。
Cosmological alpha attractors give a natural explanation for the spectral index n(s) of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial role of the hyperbolic geometry of the Poincare disk or half plane in the supergravity construction. These geometries are isometric under Mobius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kahler potential frame that explicitly preserves this symmetry, enabling the inflaton to be light. Moreover, we include higher-order curvature deformations, which can stabilize a direction orthogonal to the inflationary trajectory. We illustrate this new framework by stabilizing the single superfield alpha attractors.