Reconstructing the inflaton potential from the spectral index
Reconstructing the inflaton potential from the spectral index
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DOI：
10.1093/ptep/ptv090
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发表时间：
2015-04
影响因子：
3.5
通讯作者：
T. Chiba
中科院分区：
文献类型：
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作者：
T. Chiba
最近的宇宙学观测与标量谱指数ns符合得很好，其中ns 1 2=N，N是e折叠的数目。二次混沌模型、Starobinsky模型以及连接它们的希格斯粒子或-吸引子是预言这种关系的典型例子。我们考虑相反的问题：给定ns作为N的函数，什么是inaton势V（）。我们发现，当ns 1 = 2=N时，V（）在慢滚近似中要么是tanh 2（= 2）（“T模型”），要么是2（混沌化）到首阶.是N处1=V的比率！1的斜率为1=V，并且与-吸引子中的““相关，2 = 2=3。张量与标量之比r = 8=N（2 N + 1）。还讨论了再热温度的影响。我们还导出了ns 1 = p=N的公式。我们发现如果势能是
Recent cosmological observations are in good agreement with the scalar spectral index ns with ns 1 2=N, where N is the number of e-foldings. Quadratic chaotic model, Starobinsky model and Higgs ination or -attractors connecting them are typical examples predicting such a relation. We consider the problem in the opposite: given ns as a function of N, what is the inaton potential V ( ). We nd that for ns 1 = 2=N, V ( ) is either tanh 2 (= 2) ("T-model") or 2 (chaotic ination) to the leading order in the slow-roll approximation. is the ratio of 1=V at N!1 to the slope of 1=V at a nite N and is related to " " in the -attractors by 2 = 2=3 . The tensor-to-scalar ratio r is r = 8=N( 2 N + 1). The implications for the reheating temperature are also discussed. We also derive formulas for ns 1 = p=N. We nd that if the potential is