arXiv 1504.076922015-04astro-ph.COgr-qc

由谱指数重建暴胀子势

Reconstructing the inflaton potential from the spectral index

Takeshi Chiba

备注：: 15 pages, 3 figures, published version
发表信息：: PTEP 2015 (2015) 7, 073E02
DOI：: 10.1093/ptep/ptv090

摘要：

最近的宇宙学观测结果与标量谱指数$n_s$和$n_s-1\sim -2/N$吻合得很好，其中$N$是e折叠的数目。二次混沌模型、Starobinsky模型以及连接它们的Higgs暴胀或$α$ -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$n_s$作为$N$的函数，什么是暴胀子势$V(ϕ)$。我们发现，对于$n_s-1=-2/N$，$V(ϕ)$要么是$\tanh^2(γϕ/2)$（“T-模型”）或$ϕ^2$（混沌膨胀）的领导秩序在慢滚近似。$γ$是在$N\rightarrow \infty$处的$1/V$与在有限$N$处的$1/V$的斜率的比率，并且通过$γ^2=2/3α$与$α$吸引子中的“$α$“相关。张量标量比$r$是$r=8/N(γ^2 N +1) $。还讨论了再热温度的影响。我们还推导了$n_s-1=-p/N$的公式。我们发现，如果潜在的是有界的从上面，只有$p>1$是允许的。虽然$r$依赖于一个参数，但谱指数的运行与它无关，这可以用作$n_s(N)$的假设关系的一致性检查。

英文摘要：

Recent cosmological observations are in good agreement with the scalar spectral index $n_s$ with $n_s-1\sim -2/N$, where $N$ is the number of e-foldings. Quadratic chaotic model, Starobinsky model and Higgs inflation or $α$-attractors connecting them are typical examples predicting such a relation. We consider the problem in the opposite: given $n_s$ as a function of $N$, what is the inflaton potential $V(ϕ)$. We find that for $n_s-1=-2/N$, $V(ϕ)$ is either $\tanh^2(γϕ/2)$ ("T-model") or $ϕ^2$ (chaotic inflation) to the leading order in the slow-roll approximation. $γ$ is the ratio of $1/V$ at $N\rightarrow \infty$ to the slope of $1/V$ at a finite $N$ and is related to "$α$" in the $α$-attractors by $γ^2=2/3α$. The tensor-to-scalar ratio $r$ is $r=8/N(γ^2 N +1) $. The implications for the reheating temperature are also discussed. We also derive formulas for $n_s-1=-p/N$. We find that if the potential is bounded from above, only $p>1$ is allowed. Although $r$ depends on a parameter, the running of the spectral index is independent of it, which can be used as a consistency check of the assumed relation of $n_s(N)$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文